It is beyond me why everyone assumes perfect pitch is such a wonderful thing. The nearest visual equivalent would be if everywhere you went, you saw a Cartesian plane projected onto the landscape which told you the approximate dimensions of everything you were looking at. While this might amuse people at parties ("Hey Osbert! How high is that mountain out the window?" "157.2 metres." "OMG THAT IS SO COOL DID YOU HEAR THAT EVERYONE HE DIDN'T EVEN NEED A TAPE MEASURE"), it would also tend to take some of the aesthetic enjoyment away from life.
There are also problems of practicality. When I sing with less skilled choirs, I am forced to transpose the music down a semitone when the ensemble begins to go flat. And you can imagine what mental gymnastics I have to go through in order to perform at A-415.