If there are several pages on a domain, and they are optimized for different keywords, will google award less importance to each of them than if there was only one prevailing keyword on the whole domain?
No. Where did you hear that?
If you check wikipedia, or any other site with a lot of pages about specific keywords, you will find that all of those pages rank pretty well. In fact, if you search google a lot, wikipedia and similar sites will probably pop up in your results.
I don't think that would happen if pages got ranked less for having multiple keywords.
Also, why would Google do that? They would be essentially forcing webmasters to create a different site for every keyword. That would be awful to encyclopedias and other good sources with lots of pages that Google wants to get in their search results.