Just counting the times someone requested that particular UUID could indeed work — provided you don't store which IP requested that UUID-endpoint anywhere on your webserver or elsewhere, because then we could infer that relationship again. So this sounds like a good idea.

Is this what you originally meant?

Nontheless I hope you can see in which way the whole thing is still deeply connected to the legal question of how one can still learn about their service without tracking single users when they don't give their consent, maybe now even via DNT header.

Yes, you get more persistent attribution data for ad campaigns/whatever without consuming any personal information.