Any serious student runs their own work through detection tools before submission. A student who’s work I was reviewing was telling me that the student university actually encouraged this.

That is busy work that should neither be necessary nor encouraged.

I’m suppose the depends on who wrote it, the student or an AI.

This is actually common advice given at major universities in the UK. This was standard advice even seven years ago. Students may inadvertently plagiarize, and likewise, they may also inadvertently self-plagiarize. There's a lot of nuance that you may not have accounted for.

If this were available for free, it sounds fine. If not, then I can see this as a problem.

Personally I never found a free tool that did that and would be weary of using any that did for fear of my work being stolen and resold.

Also fuck Chegg. I will never give them a dime after they tried to take over every citation tool on the whole god damn web.

It should also be worth mentioning that AI development is specifically optimizing to reduce the difference between human and AI generated texts. In the end it is simply a rat race that the tools for detection won't win as there won't be a conclusive difference.