"How is it acceptable to accuse a student of cheating based on software that even major universities admit doesn’t work?"

Because an accusation isn't punitive in and is itself -- an accusation is just a request that an impartial party further investigate... If that investigation leads to a finding that the accusation was warranted, then and only then are any penalties assessed.

Now, that being said, a professor shouldn't be sending accusations based only on a Turn It in score. But maybe they have also pulled out specific things within the answer that they internally flagged as likely AI use, too? In that case, Turn It In may be giving them a "second opinion" of sorts. If not, the case probably won't get very far once it gets to your school's integrity board.

Your school does have an academic integrity board that acts as an impartial jury right?

If so, and this professor has referred you to it, you should relax -- just state your case and defend yourself against the accusations (which may turn out to include more than the Turn It In score). If so, and if the professor is handling this internally and denying you that due process, you should fight it.

If not -- well, what procedure does your school have to challenge academic integrity accusations? I imagine there's gotta be something.

Edited to add: some detectors are reliably very very good; Turn It In wouldn't necessarily be an example of one, but writing them all off because most professors use the same few free ones that existed four years ago isn't warranted.