The quick answer is Yes, of course Setting still matters. I won’t deny for a moment that when I’m working on a design, I feel the System > the Setting, but they are both necessary for good play and good design. Okay, so why does Setting matter?
Well, first off the PCs need to BE somewhere. So in the very basic sense, there must be a Setting in which they exist. But that’s a non-helpful answer. Setting matters because it is the material the participants build conflict out of. Yes, the resolution systems detail how you resolve those conflicts, but the mechanics themselves don’t spell out where the conflicts come from. The Setting provides the context for the conflicts. It helps the conflicts make sense.
For instance, my game Cutthroat is VERY light on Setting. I barely mention it at all (basically I can sum it all up with “Biker gangs in the 1970’s”). But even though I just barely touch on it, that is enough to give the players all the context they need to create hilarious stories and rivalries among the characters. Take that small bit of Setting away, and everything from the Challenge to the Status Rolls to the Top Dog stop making any kind of sense. Dogs in the Vineyard’s setting focuses heavily on religion. And it is out of the religion that the characters follow that the conflicts in each town arise. Strip out the setting, and you just have a nifty way to roll dice, IMO.
So what about Setting Agnostic/Generic RPGs? Good question. I’m going to divide these two kinds of games into two camps for the purposes of this essay. The first kind is the type of game that gives you procedures for creating your own Setting. Universalis and Prime Time Adventures are examples of this sort of game. The games do not contain an exact Setting, but provide explicit rules for making your own. In fact, it’s part of the fun! The other kind of game is where Setting is implicit. For instance, the core books of ADnD2e had no official “setting”, yet it was very clear that you would be playing in some kind of fantasy world. People often point to GURPS as a game with no Setting. But I would in turn point to the insane amount of supplemental books that’s come out of SJG that deal directly with Setting elements. To say GURPS as a whole doesn’t deal with setting is absurd. It most certainly does. And each group that plays GURPS will have to deal with it in some way also.
So what’s the best use for Setting? That’s another long essay. The main thing to keep in mind when creating the Setting for your game is to make the setting elements drive the conflicts. If your Setting isn’t involved in what the characters are fighting for, then it’s time to redesign it.
PS: On the topic of Settings, the grandaddy of all settings is coming out soon: Ptolus! I've seen a few previews and from what I read and seen, I give it a preliminary thumbs up! If you're into D20, you really should check this thing out.