I love your approach. This way, you don't even have to bust the students for using AI!

It's often very difficult to tell the difference between a student that uses AI and a student that performs a traditional search of the topic and just copies facts blindly and uncritically. AI writing detectors are simply not reliable enough to serve as the basis for a charge of academic misconduct. What do you do if you accuse someone of using AI, and it turns out they just happen to write in a style that's reminiscent of AI? What do you do if someone claims they just happen to write how an AI sounds? What if someone says they just used Grammerly, so now it's ambiguous what portion of their writing is their own? Academic misconduct and AI gets very thorny very quickly.

But your approach? Brilliant. Just give them a paper whose topic you taught them correctly, but you know AI will screw up. No need to affirmatively prove the cheater used AI. Just give the cheater a failing grade on the paper, because it clearly doesn't reflect what you taught them. They have no ability to later argue that they're innocent or lie that they did not in fact use AI. Their paper simply wasn't good enough to get a passing grade.

Honestly, it's pure genius. As a fellow educator, I commend you!