I agree with you,captcha is quite annoying and there has to be a better solution.However,don't think CPU mining is the one.
There are a large number of people who access forum through their mobile devices.Does your mining idea works well with them ? Being someone who is very very considerate about their privacy,why would I want any script on the website to utilise my CPU power ? That opens to a lot of vulnerabilities.
1. Yes, users should be able to choose Captcha as alternative to POW mining for some cases like too slow devices. And they should be able to adjust
2. If you respect your privacy you should be concerned about Google's Cloudfare (collecting your IP at least), not about mining script "collecting" nothing but roughly estimated CPU power. BTW, captcha also works on scripts.
What if someone else with malicious intents increases difficulty for your nickname, intentionally making wrong attempts ? Ooops, and in order to login you need to do a couple of giga-hashes. Or, if you wish, we can do it for you, for a small amount of ether... See how it works?
Again: users should be able to choose captcha as alternative to POW. They could do this in such cases.