The best explanation for the
origin of animal sacrifice rituals
It's likely that these practices predate any religion.
You think there's a non-religious motivation for a blood sacrifice? What would that be, even in general terms?
A possible explanation is that the sacrificed animal was put out as an offering to a predator animal in the area.
The predator animal was satisfied by this, as a regular source of food, and "in return" became less threatening to those humans. Also it drove away other predator animals in the area.
There are some practices like this among animals: A predator lurks near a colony of herbivores, and they are protected by this predator from other predators who otherwise would invade the territory. The herbivores choose to remain in the location and live mostly undisturbed but lose a member to the protector predator at predictable intervals. But they are better off than if there were many predators coming and going unpredictably.
This better explains the origin of animal sacrifice rituals than just saying religions invented this for no practical reason. They originally served a practical purpose, but later became religionized. Eventually the ritual practices died out as human communities and their livestock became better protected against roaming predators. But the rituals continued on for centuries as long-established religious practices.
not a product of religion, not "made up" by priests, and not ordained by God
One suggestion seems to be that the priests instituted the practices as a trick to acquire income, in the form of animals for them to eat. So it was payment from worshipers, or money in the form of meat which was brought to the temples. And maybe also the priests shared some of this "revenue" with the rulers, who obviously could not stand by without taking their cut in these profits:
It's likely that these practices predate any religion. They obviously predate anything in the Bible or anything Jewish. The latter just adopted them from the pre-existing culture.
Where did they really originate? Why did humans start doing this?
When the priests managed to con their followers into bringing them tasty animals. God got the offal.
Why have the rituals mostly disappeared? Why don't the priests do the same thing today? That clever trick should work just as well today as it did 7000 years ago.
They haven't disappeared, and it does still work, but they have decided that cash is better.
With the end of the barter economy, priests stopped expecting payment in animals, and started taking cash, just like everyone else.
Can this really explain how animal sacrifices originated? as a way to get rich, or receive payments, in the form of animals or meat paid to the priests? and maybe over time the animal payments were replaced by cash, as currencies became invented and replaced barter?
One reason this is not likely is that it would require the priests to establish a meat market, to sell the meat to consumers generally, because otherwise they would not get rich this way. They would have to resell this product for additional profit beyond their own personal consumption, meaning establishing a meat-shop business. Instead of this they would want payment in some form of easily-converted wealth, like precious stones, diamonds, etc., which could not spoil and could be stored up for years and not require a daily commercial enterprise.
Another reason this explanation doesn't make sense is that it doesn't explain the human sacrifices, which were quite common in the earlier times when the practices originated. The human offerings were probably part of the origin. They could decrease over time, as being more unpleasant, but originally they were much more common and must have been practiced out of necessity and some reason other than just a form of gaining income or getting rich. The animal meat would be much more desirable and convenient than killing humans, and yet in the earlier time the human sacrifices were very common, indicating that it was done out of necessity because there was no other choice for gaining whatever the benefit was.
Also, there had to be a social benefit, not just a selfish profit for the priests. These practices had to be understood by the community as something the whole community needed, and done to serve a general social benefit. It couldn't have just been a trick played on everyone else in order for the priests to get rich.
But if the intended benefit was to ward off some danger, such as predator attacks, as explained at the top, then this explains why human sacrifices were sometimes necessary, for the community, when there were no animals available to offer.
If a small community of humans, settled in a village or traveling or hunting, felt compelled to put out an offering to the local predator(s), and there were no animals available at that time to offer, then a human offering might have been their only choice. So out of fear of worse consequences they had a system of choosing a victim to offer when it was necessary, and this would satisfy the demand of the predator which would then leave the community in peace and wait in the area to effectively guard the community against other predators which might show up. This might be preferable for the community, even in a case where they might be able to fight off the predator, which would cause them to lose the predator's usefulness to them in driving away other predators.
So this explains the origin of animal sacrifices, including human sacrifices, whereas just inventing these rituals to promote religion, without a practical need served, inflicts damage onto the community, and pain, whereas instead they could invent something harmless and painless to satisfy their religious instincts. Religions have done this for centuries, being creative, building shrines and doing art and music, etc. to please the god(s), worshiping in many ways, without the need to do something painful and sadistic to the community.
The rituals almost certainly did not originate from religions as part of the worship of gods, because religion, as we understand it, probably came later than animal sacrifice practices. Prior to 10,000 BC it's not clear that religion really existed, outside the burial practices, which might have served a purely practical need. From 10,000 onward there emerge the clearly religious practices, large meetings with preaching and various ritual observances. The much earlier burial practices could have been done for practical purposes only, without a religious need being served.
Even if there was some form of "religion" going back to 50,000 or 100,000 BC and earlier, it's hardly what we mean by "religion" today, and obviously had no ideas about "blood atonement" or angry gods demanding sacrifices to atone for sin. So any such ideas or thinking cannot explain the origin of animal sacrifices, which probably existed much earlier:
The earliest evidence of animal sacrifice, however, comes from Paleolithic hunters who preceded Neolithic cultivators by tens of thousands of years.
The Perennial Dictionary of World Religions, p. 638 (originally published as Abingdon Dictionary of Living Religions)