I don't mean all results that may or may not even have the search terms (which is what Google "helpfully" tries to do), but all results that actually have the given search terms. Hopefully this will mean users learn to use more specific search queries to get what they want, and thus ask more specific questions --- not a bad thing at all for the Internet and society in general either.

The biggest advantage of a random ranking IMHO is that it completely eliminates any incentive to game the ranking system, and gives the "indie" portion of the Web a fairer chance at getting visitors. Let the users decide themselves individually what's relevant to them, and not Uncle Google.