I think the biggest problem in these kinds of shooters is a lack of appropriate context. This is one of the reasons I prefer WW2 shooters to most modern fare; while they share a lot of the same problems, the WW2 setting at least affords a clear, albeit shallow reason: Nazis are evil, and therefore must die. As context goes, it's incredibly facile, but it's solid context nevertheless.
I enjoy shooters, though I'm not very good at them, and several of my favorite games have been linear, so I guess I can't object to the mechanics (aside, of course, from a troubling habit of gadget cockteasing. I'm looking at you, Codblops 2). But I just can't really enjoy any modern military shooters because almost all of the time, I can't think of a single good reason why I need to be committing these acts of violence. And truthfully, I can't imagine a way to actually address the issue head-on. The enemies in this kind of game, by its very definition as "modern," have to be human, and I've never been able to get involved or be entertained by a game that commands me to murder a fellow human being and doesn't tell me why in a way that I can understand and sympathize with. Games like Dishonored get a pass, because you can complete the objective without killing them. Games like inFamous and Arkham Asylum get a pass, because you're knocking them out (and in inFamous' case, if you actually kill them, you're explicitly called a dick). Games like Bioshock get a pass, because there's very little left that's human about the enemies. But games that specifically demand unprovoked murder in order to complete a mission just don't really entertain me.
Spec Ops has probably been mentioned ten million times, but it bears repetition, because I think that's really the only you could supply real context in this kind of game. it knows that actual human beings have families, childhood memories, and all kinds of inconvenient moral protection to player characters mowing them down by the hundreds, and so it calls the player character a monster for doing so.