A posted question is a portal to information: the words and phrases it contains; the tags applied to it; the contents of any answers; and even its net votes and status (CW, etc.) are searchable. Remember, a duplicate question doesn't disappear: it remains visible and serves as a way for people to find the information they seek.
The network of pointers to duplicates enhances this "syntactic" web. By connecting apparently different questions to common answers we provide indications to the site, as well as to future users, about sometimes deep and surprising connections. This is the beginning of a semantic web.
Only people--and experienced people, working creatively towards a common goal--can create these semantics. These connections are things we should value, work to create, and curate carefully.
These considerations suggest to me that we should be spending more time identifying duplicates and building up this valuable information. Creating a single pointer to a thread with a good existing answer is far better than providing a new answer.
It is unfortunate that the SE system provides no rewards for this behavior (there are no badges or points for identifying duplicates, alas). I therefore want to thank Peter Flom for raising this issue and especially to thank all those unrecognized members of our community who have been cleaning up the tags, identifying duplicates, editing posts, and doing the hard work of building the connections that make this site ever more valuable.