But completely unrelated ideas don't spawn the kind of creativity that is really useful.
I completely disagree. Intelligent people from differing fields getting together will yield creativity on par or better than when everyone from the same industry gets together. Unless your idea of useful creativity is 500 Bay area companies doing web feed readers from back a few years ago or everyone working on Facebook apps now. Alot of really great tech ideas don't come from the Bay area. You may not hear about them, but they are out there. So maybe your premise should actually be stated as:
"if you want to come up with an idea that everyone in the Bay area will like, than you should move to the Bay area."