Well, sort of. They're not for secutiry, that's for sure. They were originally about making it harder for automated bot requests to go through and overload the server. ReCAPTCHA then started turning it around to make OCR better using machine learning, which is commonly agreed to be a Good Thing since it helped digitize old books and things like that. But of course, this in turn made it possible for bots to get past the CAPTCHA, and everything spiraled from there.

At some point everyone kind of forgot the real point of a CAPTCHA, and it's now much more of a free training data generator and much less of an obstacle for bots. But it still can prevent complete rookies from making thousands of requests per second with a simple python script, so it does serve a little bit of that original purpose.

The last one is popping up as age verification. And it's done with a camera now because otherwise anyone just sends in an AI generated picture of a face, and people don't trust companies with government id.