Depending how demanding the “real” website would be in comparison. I doubt the answer is millions.
The one service I regularly see using something like this is Invidious. I can totally get how even a bit of bot traffic would make the host's life really hard.
It's true a captcha would achieve something similar, if we assume a captcha-solving AI has a certain minimum cost. That means typical users will have to do a lot more work, though, which is why creepy things like Cloudflare have become popular, and I'm not sure what the advantages are.