Earlier quoted context omitted.
I get where you're coming from. Here's an interesting thought: consider this as an alternative to advertising. Which would you rather: a website use your mind by taking your attention to an advertisement, or a website using your CPU?
Advertising, no contest. Annoying, intrusive ads I have no qualms about adblocking, because they will never actually get me to buy a product. Helpful, non-invasive ads and clearly disclosed affiliate links? Feel free, since I'm getting some benefit too. There is no way for me to benefit from you using my cpu (ignoring the actual content in this comparison, obviously).
Would it change your mind if you were given a portion of the bitcoins generated while you were on a site that was doing this?