You can have a very hard captcha that bots cannot solve, but that discriminates against the disabled. This gives you privacy and abuse-prevention, but not accessibility. You can have a very easy captcha (or possibly multiple alternative challenges), but bots can solve those easily. This gives you accessibility and privacy, but not abuse prevention. You can mostly have easy, accessible captchas, but rely on invasive tracking and fingerprinting, this gives you accessibility and abuse-prevention, but not privacy. There's no way to have all three.
As AI gets better, traditional captchas get more and more useless, and you need more and more tracking. We'll probably reach a point where there's no task that computers can easily verify but AIs can't easily perform, except being "vouched for" by a company that the website owner trusts.