Incidentally, you still need rate-limiting if you use Google's CAPTCHA. If you don't rate-limit CAPTCHA endpoint, an attacker can DDoS you (especially if your server-side captcha component uses low-performance single-threaded HTTP client). Furthermore, an attacker within the same AS as their target can purposefully screw over their account by performing attacks on Google's services until the reputation of the network hits rock bottom.
Conveniently, normal users with typical browser configurations get nothing but the animated checkbox. For nearly everyone, the whole experience is simple and easy. The only people who get inconvenienced are the low-grade privacy enthusiasts who think that preventing tracking is the path to Internet safety. Ironically, "tracking" is literally the mechanism by which legitimate users can be distinguished from attackers, so down that road lies a sort of self-inflicted hell for which the only sensible solution is to stop hitting yourself.
"Be a good little sheeple and do what Big Brother Google says." Fuck no.