I think the dwarves should be able to reprocess clothing because I think they should be able to reprocess anything; being able to take things apart and put them back together in general seems to be a trait dwarves should have, and as people have pointed out there's plenty of historical precedence for ragpicking. Also, players have a tenancy to throw dwarves into extreme situations where reprocessing would seem less out of place--while a medieval city might not recycle their enemy's clothing in an organized way, twelve dwarves living in the side of a zombie-invested glacier might.
But Jiri is right, in that basically forcing the player to do so on a large and organized scale just to keep FPS down doesn't really make sense. For one, scavenged cloth should either be of low quality or require some sort of extended bleaching process (maybe another use for lye?). Second, and importantly, the piles of dead goblin clothing should disappear by themselves if the player clooses not to claim them. Fabric exposed to the elements should start degrading within a few months, and disappear completely within a year or two. I'd like to see Kobolds get more involved too, zeroing in on unguarded piles instead of trying to sneak through the front gate every time.
In other words, the option to scavenge and reuse enemy clothing should be there for those who want or need it. But it should bring in a low value or have some other disadvantage. Ideally, a prosperous fortress won't even bother, letting lesser races and mother nature take care of the refuse instead. Maybe even have poor, idle dwarves do the same thing individually, to raise a little extra cash (although the economy will have to be much less broken before that would be worth anyone's time).