This can thus be circumvented by an intermediary that happens to release the output somewhere. Since you don't need permission from the copyright owner to train models, you just.. take it from their website or something. As long as you don't accept their terms of service, there is nothing they can do.
Additionally, different jurisdictions take different views on browsewrap and clickwrap agreements. Usually terms of service regulate acceptable use of the website, don’t spam, don’t harass other users, don’t use bots, things that the website has a legitimate interest in.
Attempting to control what users do in their own time with public domain information from your website may be a step too far for a click or browse wrap ToS.
