It is very convenient, isn’t it? (Unless you have perfect pitch.) There’s standard guitar tuning most players know and use everyday, so when I improvise in Bb, I don’t think where the tonic is on the neck, I just know and see it instantly, in any position. Also, for most players some keys are simpler to think and play on guitar than the others. E minor, A minor are easy keys on guitar, and chances are an average player knows them on the neck pretty well.
Now you tune your guitar half step lower, and A minor sounds like G# minor (five sharps) or Ab minor (seven flats). E minor sounds like Eb minor (six flats). For me, this makes a big difference. Although I know Eb minor on the neck in standard tuning, but it would be very confusing, let’s say, to read Eb minor notation and transpose it to E minor on-the-fly in order to play in on lower-tuned guitar correctly. It is much easier to treat the sounds of Eb minor like E minor, because the fingering is still E minor. Third degree of this minor is still on 3rd fret of 6th string, or 8th fret of 2nd string etc. You can tune your guitar higher and E minor will sound like F minor, but I guess it is easier to still treat it like E minor because of familiar fingerings, chord shapes and clichés. Doesn’t matter how it sounds. It is just easier to think and play.
Again, unless you have perfect pitch. I’ve a friend of mine who is a French horn player with perfect pitch, and he told me that he had difficulties with written/concert pitch on French horn when he started this instrument. Another perfect pitch guy had difficulty playing an upright piano in a class because it was tuned some half step lower. However, when I played clarinet, I, not having absolute pitch, had no problem switching between Bb clarinet (sounds whole step lower than written) and Eb clarinet (sounds minor third higher than written). The instruments have different tuning, but the fingerings are identical, and that’s extremely useful in practice.
Capo is probably a different story. Everytime I use a capo (and I use it quite rarely), I’m still not sure how to think of what I finger on the neck. Maybe that’s because I see position I’m playing, with those dots between frets, and these things can be hard to ignore. Also, if I put the capo on the 7th fret, for example, and play E major shape, I sometimes feel it’s kinda difficult to ignore the pitch and think of it as E major, because it sounds a bit too high.