I dont know about applying to residencies. There are two reasons I have mine. ONe, I didnt know if I wanted to go to med school or law school. So, instead, I went to grad school in something that I thought could eventually be useful in either field. The second reason is because it was free AND I got a stipend for doing it (from the institution).
Maybe part of the reason i feel like its worthless is because I went straight from there into med school so Ive had little chance to see its worth in the work force or the opportunities that it may afford me.
As for now, its worthless.