rate-limiting is not what captcha does, that's for DDoS protection and even in that scenario I feel HashCash and crypto mining is a very terrible idea.
Not necessarily. If the goal is to reduce bot activity, captchas and hashcash are two ways to do that. Captchas are hard for bots to pass, whereas hashcash wastes a fixed amount of CPU time. The result is that robot operators have to invest more effort to abuse your service at scale than they're willing to (hopefully). In this sense, hashcash is a captcha alternative—it's not a captcha, but it helps with the same problem. An alternative captcha might be using something other than reCaptcha. At least, that's how I'd interpret it.