Websites aren't really fungible like that, and where they are (like general search indexing for example), that's usually the least hostile sort of automated traffic. But if that's all you care about, I'll cede the point.

Usually if you're going to go through the trouble of integrating a captcha, you want to protect against targeted attacks like a forum spammer where you don't want to let the abusive requests through at all, not just let it through after 5000ms.

One page with POW vs another identical one without POW where everything else is the same.

So it's the same as a sleep()

No, because the bot can just also sleep and scrape other sources in that time. With pow, you waste their CPU cycles and block them from doing other work.