124,
When you do High School Band, College or what ever. Nothing, I mean nothing, is written for horns in E, A, not much D, no body not even strumming guitar players delight playing anything in B, or F#. LOL!
Those keys call for all of the accidental notes on saxes, oboes, clarinet etc. which are all of the extra side keys on these instrument. I played my share in E, and A with guitar bands. But all of the groups with a pianist played in the key of C, F, G, Bb, Db, Eb Ab keys etc.
See, I knew I was an oddball. As I've said before, I know squat about saxes - apart from the fact that you blow in one end and sound comes out the other, but please don't misconstrue that as my having no appreciation for the virtuosos on that instrument - I've mentioned my sax heroes in previous threads. Anyhoo, as a keyboard guy, I'll go all day in C D E F G A (B is not even on my radar), but anything called something # or b I'll stay clear of. It's just the way my hands work.
On improvisation, like Tony Mads I`ve been 'in the water' for 50-odd years and I can paddle, but I know I`ll never be a AAA swimmer like Bill Evans. Laziness? Probably. But I get around okay, because I'm always looking for something fresh. I don't always find it, but good stuff happens along the way sometimes.