why do some instruments transpose instead of just calling the notes what they sound like at concert pitch?
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Because transposing instruments are tuned to a certain note, and the most basic way for it to produce any sort of scale is to make it play either a major scale, or its harmonic series.
Because of this, the keying system is optimized for the key. In a sense, the “basic” layout or the easiest thing you can play on them is its equivalent of “all white keys”.
And where in non-transposing instruments “all white keys” means C, in transposing instruments, it is whatever the instrument is tuned to.
So why not concert pitch?
It’s conceptually easier to think of “all white keys” as your basis and go from there.
Just like when starting out in piano and when learning new concepts in piano, you almost always do it in the key of C major. Likewise, literally music notation is based on C major, and everything else is based on how many sharps or flats they are away from C major.
So if you’re playing say an Alto sax (Eb), “all white keys” is Eb major. Having to use concert pitch (C major) as standard is hard to make “natural” to the instrument, because now you have to think in two steps: how far away am I from Eb major to get to C major (3 semitones down), then how many more steps to the key I’m actually supposed to play in?
If you transpose, and just consider the key of the instrument as its “all white keys”, then the musician only has to think once: how many steps away am I from my quote-unquote “C major”? The mental gymnastics then becomes the same as it is for non-transposing instrument players.
Also consider that players of transposing instruments tend to play different tunings of their instrument to cover range. So conceptually, it is more difficult to frame C major as two entirely different fingerings on the same key layout. A player in this framework will tend to thin “oh what’s C major concert on this instrument again?” It is easier to just think “I’m playing A major on the alto, and D major on the tenor”. While it may seem more complex because there’s two keys being talked about, again it is the concept of fingering taking over, not so much the actual pitch being produced. When keys are called out for transposing instruments, it is more of a reference to the shapes and fingering, because that is consistent between tunings of the same instrument.
Let’s actually use a non-transposing instrument to further this example. Say you have a guitar player, and he is playing a piece in C major, and his job is to play rhythm guitar, with the chords C-G-Am-F. Now hand him a baritone guitar. Despite the instrument still being non-transposing, the range and tuning is now different. Conceptually, this guitarist now is thinking, “well what is C-G-Am-F on baritone? Ah C major on a baritone is playing F major, so the chords are going to be F-C-Dm-Bb”. So as you can see, even on a non-transposing instrument, conceptually, a guitar player when switching to a differently tuned instrument thinks in transposition, because it is easier to think in other keys relative to the instruments tuning, than to plainly think in concert pitch.
TL;DR it takes less thinking to transpose than to use concert pitch for all instruments.
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