I see what you mean, roady. When I taught elementary instrumental music, I'd have C flutes, Bb clarinets and cornets, and Eb alto saxes, all playing the same scale but in different keys. Start adding flats for a new key, and invariably they'd go to the default B/A/F# that they'd learned first. It takes awhile, sometimes a long while, to get over it. But the better ones do.
At least in solo tuning, every note's "address," as Joey says, is unique, with the exception of two enharmonics. Sharps are easier (button in!) than flats to suss out. Each scale is unique, although some are very similar (C and Db, for instance). With dimi, there are only three scale patterns, which could be an advantage; but as someone pointed out, sightreading may suffer if you lose your place. And dimidude points out that LeGato tuning has many more choices on enharmonics, in which case I imagine it's best to choose a default set of scales and stick to them before venturing out into the enharmonics, especially for sightreading.
I can't think of any other wind instrument that offers so many options!
Tom