I think people want perfect pitch because they think it sounds impressive. That's why. It's hardly a good reason, but it's true.
All these people who are talking about perfect pitch people not being able to be flexible in terms of period tuning, quarter-tones, etc. and generally making themselves miserable when the choir/orchestra/instrument is not tuned to A=440, for example, let me clarify some things.
I have perfect pitch. I'm not miserable playing on an out-of-tune piano as long as the whole instrument is flat or sharp. If only certain notes are noticeably out-of-tune, I don't think I'm the only one who would be driven nuts. People with good relative pitch would be driven crazy as well.
Yes, it's true that when you first put a perfect pitch person into an acapella choir (for example), he/she will find it very difficult to follow the tuning fluctuations because the inner ear will say that it doesn't sound right. BUT, that is something that can be trained. It's just like musicians without perfect pitch training for relative pitch - they learn to sharpen their aural skills, we on the other hand learn to accommodate different tunings. It's not much different - the process is just the opposite. You can have perfect pitch and relative pitch at the same time. You can learn to 'hear' individual notes and intervals at the same time. It's not a case of "you can only do either this or that".
When I sing in a choir, especially for early music, I read more of intervals rather than individual notes. It hasn't caused me much misery at all. On the other hand, if we're singing a highly polyphonic composition (early music or not), I can easily sound the first note of each entry in my part, and keep the others in tune. It's for that reason that I'm placed at the edge of my section - because I won't be easily pulled away by the other parts.
And then, having perfect pitch means that all my aural tests for music examinations are a breeze. I have no problems naming cadences, keys, modulations, etc. because I know what notes the examiner is playing.
I'm a string player as well. It's precisely because I hate playing out of tune, that I ended up being one of those with above average intonation when I played in school orchestras and my music exams. I reckon that's a good thing.
I definitely think having perfect pitch AND good relative pitch at the same time is a good thing. But if someone only has perfect pitch and refuses to learn relative pitch, well then it's the person that's the problem, not the ability.