We have this habit in FLING (one of the bands I play in) to get into protracted email conversations about a variety of subjects when we're not together rehearsing or playing. Recently, Mike, one of our guitar players, pointed us all towards this 15-minute YouTube video about learning music theory. Mike's an awesome guitar player who learned his craft with both some private lessons as well as just learn-it-yourself dedication (and if you haven't heard FLING play, you owe it to yourself to soak in one of Mike's killer leads). It was interesting to me that someone this accomplished wouldn't have been taught some theory along the way, but the more I thought about it, this actually makes sense.
As someone who's taken quite a few years of harmony and theory in school and also dabbled in piano and guitar enough to be incompetent and dangerous on those instruments, I've come to the following conclusion:
Key signatures and, indeed, sharps and flats, are a piano-rooted construct that has become the common language for our conversations and communication about music. When applied on guitar — when learned on guitar — they don't make a whole lot of sense because everything looks equal on the fretboard. On piano, of course, sharps and flats are (for the most part) the black keys, and provide a much simpler and quicker way to visualize and learn the basics.
Because of this I highly recommend even just a year (or maybe even less) of theory-based piano lessons for all musicians simply to muck with and grok these concepts quickly and visually. It gets a lot of the legwork out of the way and then you can come back to guitar, etc., and understand how silly it is to try to learn these things there. On guitar, for example, going from an E to an F is one fret, but going from an F to a G is two frets. How in the world is that supposed to make sense to someone who doesn't first understand that this is a piano-based concept where going from an E to an F and an F to a G both mean that you're just going up "one white key." The only difference is that, oh yeah, between the F and the G there's this black key that doesn't exist between E and F. On guitar they're all treated equally in a visual sense.
Anyway, there's my pitch for some (theory-based) piano lessons for all musicians.