Moving away from a fairly strict focus on multiplayer and your typical war settings might help. Folks used to complain about how World War II as a setting was run into the ground, but war in general feels so terribly generic these days. There's plenty of opportunity elsewhere, even if it's a story-driven title that focuses on a more personal experience, à la BioShock.
War shooters should still exist as quite a few people like 'em, but there are far greener pastures that've yet to be explored for no good reason.
I'd rather they go the other way, scrap singleplayer completely, and focus on making the best possible multiplayer experience possible.
Some people just don't get the appeal of multiplayer FPS games and think it's just about people running around like headless chickens endlessly killing each other. It's really not. For a lot of people, the appeal of multiplayer FPS games comes from joining clans and competing in serious leagues and tournaments. The problem with recent COD and Battlefield games is, they really haven't done a good job of supporting this style of gameplay. Instead, they dangle a carrot in front of the player in the form of ranks and unlocks and encourage very anti-social gameplay. You're expected to work towards your own goals, get bored, and move onto the next annual release.
In actual fact, there needs to be both. Exclusively single-player FPS games with a really deep and involving story, and exclusively multiplayer FPS games offering the best online experience possible. I hate how developers feel the need to produce both for one game - and that goes for a lot of genres, not just the FPS genre.
As for the setting, I kind've agree... WW2 was exhausted, and now the same has happened to modern warfare. Getting rid of war entirely isn't necessarily the solution... they just need to get more creative - like making up wars along with completely fictional weapons. The main thing is, it doesn't have to be futuristic to be made up.