Absolute (“perfect”) pitch is, for some people, a kind of shorthand for supreme musical giftedness…when in reality it’s more of a curious party trick than a skill that is valuable for a musician or composer. So you can train yourself to do it—what’s the point exactly? Plenty of people who don’t have that skill have an extremely accurate ear for relative pitch, which is the one that actually matters.
I don't think it's just a parlor trick. (I don't have it, BTW.) Obviously it depends on the instrument: for example, if you're playing the piano you can completely forget about absolute pitch. But if you're singing a long passage without accompaniment, without absolute pitch you may end up drifting.
Also, a lot of classical composers enjoyed elaborate key changes: e.g., you'll have your main theme in A major, and then it appears again in D major, and later it comes back as A major. If you have absolute pitch (those composers likely did), then they all sound different, as if you first see a picture in black and white and later it comes back in blue. If you don't, then that part of composition completely passes over your brain.
> But if you're singing a long passage without accompaniment, without absolute pitch you may end up drifting.
You don't need absolute pitch to not drift.
You just need to maintain relative pitch. That maintenance requires attention and some practice, but it doesn't even remotely require absolute pitch.
And remember that singers with absolute pitch have their own problems, in that singing the same song when accompanied by a new piano that is tuned slightly differently becomes much harder and annoying. Whereas for most people they don't notice and sing in tune with it effortlessly.
Also, people with relative pitch certainly experience key changes, the sense of tension introduced by a new one, and the sense of "returning home" and relief when you go back. Composers write for that sensation which is shared by everyone. Not for any kind of absolute perception. And I don't know why you think classical composers overwhelmingly had absolute pitch. Do you have any evidence?
> Also, a lot of classical composers enjoyed elaborate key changes: e.g., you'll have your main theme in A major, and then it appears again in D major, and later it comes back as A major. If you have absolute pitch (those composers likely did), then they all sound different, as if you first see a picture in black and white and later it comes back in blue. If you don't, then that part of composition completely passes over your brain.
Even if one doesn't have perfect pitch they'll still notice the key change itself unless it's performed very subtly or after a long pause. If the key change is drastic enough the timbre of the instruments will change as well resulting in a different sound.
It can also hurt in some situations. I have absolute pitch, and used to sing in a choir. Sometimes the director would decide to use a different key than the one written on the sheet music, which meant that I’d have to transpose in my head in real time.
Absolute pitch is frequently a nuisance. American orchestras tune to A=440, but in Europe A=442 or A=443 are more common. Analog recordings often deviate significantly from any pitch standard, either due to inaccuracies in tape speeds or due to a deliberate stylistic choice. These variations are completely unnoticeable to someone with good relative pitch, but can be a source of confusion or discomfort for someone with absolute pitch.
Just to provide a data point here, I have absolute pitch (from a very young age) in that all the different notes FEEL different in an incredibly obvious way the same way different animal noises feel different. I have no issues identifying chords played on pianos, even somewhat dissonant ones. Listening to slightly detuned orchestras doesn't bother me at all. I probably can't tell 440 from 432 or whatever.