To what end? Not cheating on the weekly assignments is surely more beneficial to learning than cheating on them is, but I don’t see how removing the assignments altogether would help students learn.
It's a crude blade to avoid the issues of AI pollution of weekly submissions, of which few teachers have much confidence that the submission itself was actually written by the student - who's assumed to be learning something.
The OP was about students dumbing down their own work to avoid AI detectors ratting them out. That seems like a big loss.
And what would the goal of that be? I thought the goal of education was... education. The grading is not goal in itself. Will this really motivate kids to do better?
It's to prove that a student is actually educated and has a firm grasp of the course material. If one gets an A every week on AI-assisted submissions, can one make such a claim? And can a teacher make the claim that they've achieved any actual education of the student?
A grade, on a single proctored test, is a crude metric, but at least it would be a brutally fair one.