We have evidence uniquely in the case of the reported Jesus miracle acts, but in no other cases.
Your entire “logic” is predicated on the notion that there existed a first century equivalent of a newspaper of record that reported—for all posterity—on officially investigated “hoaxes” and/or reported every single idiotic claim that any person made, such that they could in turn be investigated and tracked.
No such fundamental record existed.
I'm not asserting anything which assumes such a record existed.
There were at least two authors who tell of fraudulent miracle-worker charlatans -- Josephus and Lucian. Most of the charlatans they describe are unknown to us outside the accounts of these writers. Of the reputed wonder-workers of the period, in the literature, a large percentage are among these charlatans reported by Josephus and Lucian. So it was normal for reputed miracle-workers to be made known to us by writers who reported them as frauds. (This changes after 200 AD as the stories increase and become more sympathetic to the miracle claims, but prior to that the sources more commonly report them as fraudulent.) Plutarch also criticizes some of the fraudulent practitioners.
So there's much mention of reputed miracle-workers who were hoaxes, during this time, but virtually no mention of miracle legends taken seriously by the sources reporting them. The few exceptions to this are easy to explain as fiction stories. But there is no way to explain the Jesus miracle acts as fictional, given the accounts and the proximity to the reported events and the lack of any explanation how Jesus could have become the object of mythologizing such as famous and powerful figures like Alexander the Great or Emperor Vespasian were mythologized, or how people could have mistaken Jesus to have divine healing power when he did not cite any ancient healing god as his source of power, as all the other healer-practitioners had to do in order to win their public reputation.
Second, there are no primary sources making any such claims.
There are virtually no "primary sources" making any claims of any kind. History is based on the sources which exist, not on imaginary "primary sources" you wish existed. Our sources for the Jesus miracle acts are better than our sources for most of the ancient history events generally. There are reasons one might doubt the reports, but the complaint that there are no "primary sources" is no more reason to doubt these reported events than 90% of the reported history of those times.
There are only stories of stories handed down year after year in oral form until decades later (at best) some unknown author (“Mark”) wrote his version.
And that's a better and more reliable account we have for an historical figure than we have for any other 1st-century Jew or 1st-century figure living in Palestine. Except Josephus, and for him we have nothing but his own writings.
Most of our ancient history record was written decades later, even 100 years later, and is based on the oral stories handed down. Only a small percent is from authors contemporaneous to the events.
The closest we can get to any confirmed identity of any of the authors of the NT is Paul, who never met Jesus (in spite of the fact that he supposedly lived contemporaneously to him and was both a Roman citizen and a Jew).
That's better than we have for most historical figures reported in the writings, until 1000 or so years later when accounts began to be written closer to the reported events.
That the "identity" of the authors is not "confirmed" has nothing to do with the credibility of the reported events. There are other anonymous writings which are relied on for the historical record. Though most sources have a named author, that doesn't magically make the accounts more credible.
Third, the claims are not just that Jesus could perform miracles, but that his disciples could as well, including raising people from the dead.
There's almost nothing in the Gospel accounts saying that. It's only the
Book of Acts reporting those events. Those later stories were obviously inspired by the earlier Jesus miracle accounts. Since they can easily be explained and since there's only one source (
Acts), there's much less credibility to those later stories. But there is no explanation what inspired the Jesus miracle stories unless they were real events.
If we can easily explain miracle stories as fiction, accounting for what caused the stories, then they are much less credible. But where there is no explanation of what caused the stories, a good explanation is that the events really did happen.
Yet, curiously, there is not a single mention of any such resurrection either in any of the books of the NT or external sources, which one would think would be significantly news worthy to actually instantiate a working press.
Miracle acts by the disciples, reported only in
Acts, are probably fiction and were not widely believed until much later.
Fourth, the fact that there were (supposedly) 12 disciples walking around Jerusalem with the power to heal the sick and raise the dead makes one wonder why those people are not still alive today.
There's virtually nothing of this except in
Acts. Claiming to "heal the sick" was common just like today when believers pray for each other to recover from illness (and either don't recover, or they would have anyway without the praying). The only serious healing stories, outside the Jesus miracle acts, are in
Acts, and there's no reason to believe these which are mostly copycat stories inspired by the Jesus miracles. The existence of these later healing stories is explained by the earlier Jesus miracle acts, which are the beginning of an explosion of miracle stories appearing at the end of the 1st century and increasing into the 2nd century.
The explanation for all this is that the Jesus miracle acts really happened, and this then inspired the new unprecedented explosion of miracle stories going into the Middle Ages. But if the Jesus miracle acts never really happened, it's impossible to explain what caused this new explosion of miracle stories to take place.
Was there a statute of limitations on their powers?
They didn't have such powers. The disciples never did perform those miracles reported in
Acts. Those are stories inspired by what happened earlier. Believing the Jesus miracle acts happened is based on evidence = 4 (5) sources near to the alleged events. We don't have such evidence for the stories in
Acts, nor for any other miracle stories of antiquity. It's reasonable to distinguish between those accounts for which there is evidence and those which follow the normal pattern of mythologizing and storytelling. It's not reasonable to lump all miracle stories into one category and brand them all as fiction.
If so, then why didn’t they raise ALL of their dead friends and relatives, let alone, you know, Moses or the like? Why not whole armies in fact, let alone just touching Jesus and healing him while he was on the cross or resurrecting him after he supposedly died?
It's easy to poke fun at the part which is obviously fiction.
But it's also easy to explain where those stories came from, as fiction. What cannot be explained is why such stories were not told 50 or 100 years earlier. Why don't we see stories of such miracles in 60 or 40 or 20 AD and earlier? There is a total blank of such stories in the literature going back at least 200 or 300 years. There is no miracle tradition in the Jewish or Greek/Roman culture during these centuries having any resemblance to the Jesus miracle healings and which could explain where these came from, if they could be explained as fiction. The Asclepius cult, the closest there is to anything analogous, was dying out, and these were priests worshiping an ancient healing god and performing rituals like modern healers who perform their rites in the name of Christ.
Which leads to the absence of evidence being evidence conundrum and actually flips your argument against you.
There are many pieces of evidence pointing to the Jesus miracle acts as real events in history, unlike other miracle legends of the period. A significant number of those other miracle legends were condemned as hoaxes and even would not be known to us had they not been reported as hoaxes by the sources. This alone doesn't prove much. But this, along with dozens more facts about miracle stories in the ancient world point again and again to the historicity of the Jesus miracle acts, unlike all the others we find in various writings and not supported by any evidence.
The reliable and neutral sources, or those exterior to Christianity, say nothing about the Jesus miracles, and almost nothing about Jesus generally. However, he is mentioned, or alluded to, and there's plenty to indicate that there was some knowledge of him, and that he is not named as another hoax is significant. If they had any knowledge of the miracle claims, they obviously dismissed them as probably untrue, as 99% of such stories were dismissed as untrue, whether the stories were investigated in detail or not.
Because no one else reported any of these miracles—except for cult members—is . . .
The Gospel writers, and Paul (who reports only the resurrection), were all believers, but we don't know that their belief was not caused by the evidence they had before them. There was no "church" as we understand it today, and there was no one "cult" of the Christ believers, but several different cults or communities which each carried on its own "gospel" mission as its members understood it. So the important question is not whether they were "cult members" or believers, but what caused them to become believers.
Did the Gospel-writers become ensnared into a Christ "cult"?
How did that happen? Any notion that they were first snagged into a Christ "cult" and programmed into believing and following the cult has little connection to reality. These writers were the most educated of all within the different Christ-believing groups, and they made their own independent choice what to believe. It makes no sense to say they promoted the miracle stories as a cult-crusader unless you first explain what caused them to become such a crusader at the outset.
They did not have a charismatic guru-prophet to inspire them.
For most cult-crusaders the cause of their loyalty and zeal is the powerful impact which the cult-leader-guru had on them, with his charisma. This explains it in 99% of the cases. But in the case of Jesus there was no such charismatic impact on these "cult" members who wrote of him, because they had never seen him directly. So then, what persuaded them to believe? What could it have been other than the evidence and corroboration before them?
The best explanation is that they had enough sources or evidence before them, in the oral reports and earlier written accounts, that they became convinced that these events really did happen, unlike most miracle claims which they no doubt were familiar with.
. . . is strong evidence that no such miraculous events actually happened.
No, it's further evidence that the events did happen, or that there was the extra evidence that they really happened, because otherwise it's impossible to explain what was the predisposition or bias to believe these stories and not the dozens of other miracle claims which were not worth reporting or wasting time on. If the events did not really happen, we'd expect someone educated to find some indication of it and report them as hoaxes (which happened with some miracle hoaxes of the time).
Why did all those educated enough to report on this come to the conclusion that the stories were true?
There is no indication that the writers were driven by their loyalty to a cult discipline requiring them to believe something fraudulent. There was no cult discipline controlling these writers and no blind faith toward any creed at this time, in 50-100 AD before any "church" yet existed and when there were diverse Christ "cults" here and there, often in conflict with each other.