What's the ratio of false positives? honestly curious

You're right.

The problem is, people (especially professors) are going to look for it no matter what.

Just look at the stats. Roberta OpenAI detector was downloaded a whopping 114k times in just last month. It clearly states not to use it as ChatGPT detector but I see a lot of it's implementations

Better to educate users with a big fat disclaimer and a tool

I'm totally aware of that and I will be putting a disclaimer in front page, not buried in a Terms and Conditions link somewhere.

The tools currently available can ruin a student's life by not explicitly mentioning it.

I want to address that issue by providing a solution that comes at top of the search and informing professors about limitations as explicitly as possible