Absolute pitch is a curse for musicians. It's not even an asset unless you are a piano tuner or a transcription professional of some sort. Not many conductors have it. Only a handful of the great musicians in history, from classical to jazz to pop happened to have AP. It's a parlor trick. And many musicians thought to have perfect pitch actually were just great recognizing pitches - pitch memory - which is different from perfect pitch. I can recognize pitches with a ~50% accuracy just because I can either recall the note, or bend my vocal chords as if I would start singing the note and, from pure muscle memory, say "this is probably an E".
Absolute pitch basically spoils the musician's ability to deal with varying pitch and musical temperament[1] situations and instruments. It can drive them nuts, ie if given a C to sing but actually have to detune or transpose it on the fly. It's also detrimental for anyone's ability to purely enjoy music. _Relative pitch_ on the other hand is so much more important. Absolute pitch in fact can mess with your relative pitch, as C and Ab are just that C and Ab, not a minor 6th.
Also, a good sense of being in tune when playing with others is, obviously, fundamental but also a relative, not absolute, in essence. Knowing you are playing in tune, not perfectly pitched, is the asset needed by bowed string players. Relative pitch, not AP, is an asset for someone who needs to sight sing on pitch - just listen to your tuning fork and find that C or Ab.
Music is not a perfect craft, it's not about being digitally precise. Making music is not about frequencies, or hitting absolute hertz. Even pitch itself is not "perfect", it's a flawed system that people, in part for the sake of standardization, settled upon. Pitch is a size that does not fit all. So why would anyone be proud of have frequencies memorized?
[1] https://en.wikipedia.org/wiki/Musical_temperament