Cellist for the last 35 years here. No perfect pitch. My "perfect" note identification is based on timbre: I know what each note sounds like on the instruments I know intimately.
For synthetic tones, I will be off +/- 3 semitones because I will be using an aural memory of the cello a string as a reference, rather than recognizing the frequency like the perfect pitch folks do.
Never occurred to me to practice perfect pitch because, as you said, it is not that useful.
Same for me on the guitar: it is easy to distinguish even the same note on different strings. Chords, too. But it's more a timbre plus relative pitch sensibility.
It is useless for everyone except singers. If you’re a singer, you can cold-start a song in tune and have the band come in seconds later. Hard to do that without the confidence that you both started correctly and haven’t drifted.
There's a story about the opera singer Kirsten Flagstad (1895 - 1962) from when she performed at a small place somewhere, singing opera songs with just a piano. Afterwards one from the audience actually complained directly to her that she didn't sing well, she was out of tune. She apologized and said that she had perfect pitch, and the piano wasn't tuned to her inner pitch - and she found herself unable to adjust to the piano.
As for singers in general, I've seen lots of professional singers who don't have perfect pitch but still can cold-start a song - they know their own vocal cords so well that they can start at the right pitch with confidence.
My experience with pitch memory is nearly identical to yours (but only 34 years playing cello, not 35).
Absolute (perfect) pitch really does seem to be a whole different thing neurally, akin to (and perhaps actually related to) the difference between learning a language before a critical age and learning one afterwards.
I'm gonna try to teach it to my kid, because, why not. Even if it's not that useful most of the time, there are definitely times when it would come in handy for me, e.g., being faster at transcribing notation from recordings. If he doesn't end up using it, that's fine.
I suggest not to do it. It is really painful in the orchestra when the orchestra has gotten sharper than what you are comfortable with and you have to play a minor third. I remember playing Mahler 2. The hall was hot as hell and the orchestra had risen from A441 to what must have been A445. I had to play a major sixth and it was borderline revolting.
I stopped practicing it after some experiences like that. Knowing what note to play by some absolute measure is only useful if you are playing alone. What you play in an ensemble is relative to a lot of other people.
Having perfect pitch can be useful for a lot of musicians, or educators, or composers in various ways, including:
Improving accuracy in performance: Perfect pitch can identify and reproduce musical notes more accurately and quickly, which can help perform music with greater precision.
Improving music education: Perfect pitch can help people teach music theory and composition more effectively, as students with perfect pitch can better understand and apply the concepts.
Enhancing creativity in music composition: Composers with pitch can more easily hear and reproduce musical ideas in their heads, which can help them create more complex and interesting compositions.
Facilitating communication among musicians: Musicians with absolute pitch can communicate more effectively with each other by using a common standard for identifying notes.
Improving the ability to transcribe music: Musicians with perfect pitch can more easily transcribe music by ear, which can be useful for analyzing and studying music.... the list goes on
I am an orchestra musician. Having perfect pitch was only trouble, despite playing in good orchestras at the time.
In the end of Ein Heldenleben the orchestra will not be the same pitch it started and, and for you to be in tune you will have to play notes that will be more than a quarter tone too high compared to what you think is correct.
I found it awful. The only orchestras I have played in that stayed in tune was the Swedish radio orchestra and the Munich Phil. But a major third is 13 cent low there as well.
And regarding most other things: I would have loved to have it during solfege exams. That is about it. The trouble it gave me when doing the work I studied to do it got in the way.
Most colleges I went to had special classes for students with perfect pitch as they were taught different strategies. In my final exam in "Gehörbildung" the two top scoring students did not have perfect pitch.
from what I understand, perfect absolute pitch is (to me) of negative value in the sense that it makes you annoyed at a lot of music. I've heard some people say it makes them not enjoy practicing pieces with other musicians. I think "why be aggravated if I don't have to?"
On the bassoon this was (and is) the case for me. It even translates to instruments very close to the bassoon such as dulcian and the French basson. If I hear a baroque bassoon I know what note it is in 415.
For synthetic tones, I will be off +/- 3 semitones because I will be using an aural memory of the cello a string as a reference, rather than recognizing the frequency like the perfect pitch folks do.
Never occurred to me to practice perfect pitch because, as you said, it is not that useful.