No, they can't. He was convicted of jack, so no court will enforce that. Again, this was a constitutional crisis that the GOP took a dump on.
What does the lack of a conviction have to do with it?
If you look at the charges brought up against Trump, I believe none of them are based on statements he made about the election or January 6th. The most critical aspect is that Trump has not been charged with inciting a riot. If the Justice Department won't charge him with that or if DC doesn't charge him with that, no Judge in this country is going to make that leap alone. In one of these threads, I linked a Legal Eagle video on the free speech issue, which was quite frightening regarding what is protected speech, and why Jack Smith has been particularly choosey on his charges against Trump.
There is no clear requirement in the law for such a standard, and if we take a textualist read of this, it's very clear that the authors made a purposeful choice not to include such a requirement.
And in a perfect world, yes, you are right. But in that perfect world, Trump was impeached in January 2021 with a near unanimous vote and the punishment included not being able to reseek the office of the Presidency. One issue you are not considering here is that of precedence. There is none for this situation. The Civil War was a pretty blatant act of treason. Had Trump gotten his wish, and went to the US Capitol and commanded certain actions, this might be a much easier case to provide precedence. But that didn't happen thanks to the Secret Service.
So we are left with absolutely no case law, and not a Federal Judge in the US would touch that to begin the process with a 42 foot pole unless it was Judge Cannon and President Biden was the defendant.
It's not as though the authors were unfamiliar with the concept of a criminal conviction. But that isn't how they worded it. Why not?
Because there was a Civil War that was just fought. The sides were well known. This was specifically about those traitors. Please don't mistake my pragmatism for anything but pragmatic understanding that Federal Judges will not unleash a process to prohibit a person not found guilty of a crime (especially a former President) from running for office. I'd imagine "standing" will be the easy way out of this case. As the violation of an insurrection isn't against a person, but the Government and the US Government might need to be the one to actually request a 14th Amendment solution, and that ain't happening either.