It's an interesting idea for sure, but in my opinion the objections are justified. The problem I (and some others here) have with this is

"I easily could have hidden it. In fact, I could install this on every site you visit, and you'd hardly notice."

Personally, I think even with the assumption that the overall goal (finding prime numbers, for example) is a worthy use of crowd sourced CPU, sneakily co-opting visitors' CPUs without their knowledge or consent in order to do it is essentially building a bot net.

"The cool thing is that I could be solving a real problem, and someone or some company could be paying me for all the work that people's computers are doing when they visit my site."

I'm not sure I'd be willing to let someone sell my computer without my consent or knowledge. If this was an opt-in thing it would actually be kind of neat, I think.