If you replace the CAPTCHA with a Hashcash-like PoW system, couldn't the server increase the difficulty when it receives too many connections from an IP? Even

If you replace the CAPTCHA with a Hashcash-like PoW system, couldn't the server increase the difficulty when it receives too many connections from an IP? Even with a huge botnet, spammers can only have so many IPs and computing power. The difficulty could easily be adjusted to have a computing time ranging from a few milliseconds on a cheap smartphone (default) to a few minutes/hours on a desktop computer (for abusers).