Is absolute pitch something you would actually want? From what I’ve read as people with absolute pitch get into late middle age in many their reference drifts and they start to perceive music that is in tune as being out of tune. For some this makes it hard to continue to enjoy music.
People with relative pitch can learn specific notes well enough to be able to recognize them given the constraint that the note is being played roughly in tune on an instrument tuned to the common tunings of the music they are familiar with, and they can learn to recognize intervals.
This allows them with practice to identify notes almost as fast as someone with absolute pitch, and allows them to do all the practical musical things people with absolute pitch can do.
Yea, absolute pitch is not very valuable for musicians. Interval training is much more common, where you train on the differences between notes (maj 3rd, minor 6th etc.). Good interval skills make improvisation and composition much easier. If you know the key you're in having absolute pitch doesn't really add anything, and if you're lacking in understanding intervals it won't make up for it.
People with relative pitch can learn specific notes well enough to be able to recognize them given the constraint that the note is being played roughly in tune on an instrument tuned to the common tunings of the music they are familiar with, and they can learn to recognize intervals.
This allows them with practice to identify notes almost as fast as someone with absolute pitch, and allows them to do all the practical musical things people with absolute pitch can do.