Yep.
There's a line in the Wiki article on Closers which reads "Former Baltimore Orioles manager Johnny Oates once told Jerome Holtzman, the inventor of the save statistic, that he created the ninth-inning pitcher by inventing the save."
To a certain extent, the save stat becomes the measure of the top relievers, and forces the top notch relief man to want to play only (mainly?) in save situations. If you're likely to keep 94-95% of your 9th inning leads anyway, then why not forego having an elite, big dollar closer on your staff, have a couple of fairly decent men, close by committee (based on L/R match-ups etc), and use the money elsewhere on the roster ?
Not an issue for the Yankees, obviously, but a possibility for other teams - which is maybe why closers are quite mobile between clubs, as El J pointed out previously.
PS None of the above explains Ryan Franklin, however, unless he just got unlucky (in baseball, a genuine statistical variation in a player's performance is almost always explained by form / blowing hot or blowing cold, rather than just being the result of chance) or perhaps he's just not that good a pitcher anyway. I can't remember ever feeling comfortable with him closing, personally, so I guess I'm now suggesting the latter.