I have perfect pitch and for most things, it is incredibly useful and a great tool. In other ways, it is a drawback. Instruments like French Horn and saxophone (and trumpet and clarinet to a lesser extent) are extremely hard to read if not impossible, because our brains cannot reconcile the difference in the sound and the note on the page.
In other words, when I press the fingering for a "D" and a note other than "D" comes out, our system crashes. While other people will accept a "C" as a clarinet "D", we can't do that....because we know better. We know that what we are really playing is a "C."
So in playing transposing instruments, perfect pitch is a massive drawback. Of course, all this could be avoided if parts for every instrument were available in concert pitch. Unfortunately that's not the case.
Now I'm a little confused, because I'm reading about people trying to learn perfect pitch. I didn't think true perfect pitch could be learnt. Even if you train yourself to be able to recall "C" without reference, you are still getting other notes based upon the "C" you remember.
Those of us with perfect pitch hear and identify every note immediately without even thinking.