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.
