There is a radio interview somewhere on-line with Milton Babbitt, in which Babbitt seriously slams Paul Hindemith for Hindemith's idea that a composer should have some facility on all the instruments for which they write. Babbitt's objection was that the limitations the individual composer has with regard to playing particular instruments would carry over to unnecessarily limiting the way one composed for the instruments.
While I'm all for the eliminating unnecessary limits on a composer's imagination, I also think think it's useful to know more rather than less about how instruments work, but I don't think that either Babbitt or Hindemith has quite got this right. Babbitt runs awfully close to defending a position of knowing less rather than more while Hindemith's position, valuing a certain established body of technique — craft — above all else, runs into Homo Faber territory, more engineering than art. I think rather more to the point is the idea that becoming familiar with an instrument as a composer is not only to determine how facile or difficult particular tasks on instruments (or voices, for that matter) might be, but to have a more intimate qualitative relationship to the instrument.
This is illustrated by a story which Alvin Lucier likes to tell about commissioning a choral work from Morton Feldman. Feldman asked Lucier about the range of the Brandeis Chamber Choir, which Lucier directed in the 1960's, specializing in a contemporary music repertoire. Lucier indicated that he had sopranos who could go so high and basses who could go so low. Feldman protested that he didn't want to know the extreme possibilities, but he wanted to know the range, meaning the range in which the choir had a consistent quality of sound, a fundamentally different idea and one that could only be answered based on the experience of working with closely with the particular choir. Likewise, on instruments, it's useful to know how a sound will be produced because it tells you something musically valuable: the tones using the open fingerholes on a flute or bassoon have a different qualities and possibilities from those using a lot of keys, for example, or the tones around the break between registers on the clarinet, which require some caution as they use either the shortest or longest lengths of tubing, and — especially with amateurs — can often speak quite distinctively as one moves between those lengths; it's useful to know that a horn player, when muting by hand, may have to modify the pitch by adding a valve; or knowing at least the basics about string fingering, and how it differs from the violin to the cello to the contrabass, which can be very useful in making passagework more clear... Now, good players may well have musically acceptable end-runs around the technical problems composers pose, but I think that it is more responsible to the practice of music to keep these to a minimum. Composers can, periodically, demand some magic tricks from players but if we want a constant stream of miracles in our scores, we have to be responsible for them ourselves.
Most importantly, I suppose, when a composer knows something about the playing technique of a particular instruments, she or he has a better basis for being able to communicate with musicians. Having just a bit of shared technique and technical vocabulary may often be enough to completely open up the dialogue with players, and the best opening is often when a composer can indicate with some precision that he or she is at the practical limits of his or her knowledge or ability and is respectfully seeking collaboration with a skilled and knowledgeable colleague, a useful step towards making better music together.