I think "unorthodox" or his favourite "maverick" are better descriptions of McCain than "moderate". Many on the left genuinely appreciated him as a senator - but of course as a presidential candidate he had to care far more about coming across as a good conservative following the party line, and inevitably lost his appeal to Democrats. I frankly know too little about Bush prior and during his first election to say - I was thirteen in 2000.

I think it's not so much that the country is looking for a centrist, as looking for a reconciliator - someone who can lessen the endless bickering and get things done with both parties (and man, was the left ever wrong when they thought Obama could be that guy...). Which obviously is a lot easier if you're a centrist, but being a centrist in itself isn't enough, and as you note the majority of both parties is lukewarm at best about centrists policy-wise.