To be honest I think first and third person shooters will remain as long as games do. Perhaps if we ever see something akin to VR (which I doubt, for reasons I won't get into again, as much as I'd like to see it) that will change, but even so it will just mean people will start VR projecting as soldiers in battlefield situations. That said, I imagine the popularity and settings will fluctuate back and forth over time. Something like "Call Of Duty" is a generic enough title where I imagine it will continue to be used for shooter-type war games in a variety of settings even if the "Modern Warfare" title dies out.
Right now the big threat to these games seems to largely be profit mongering. These kinds of games set preposterously high sales expectations to the point where simply selling well seems like a failure. Not to mention an increasingly greedy industry that is out to monetize just about everything, simply making a good game, and then selling it for a profit isn't enough now, they want a game that they can sell for a profit, and which will then continue to make them money perpetually until they release a new one. Micro transactions in multiplayer games that are allegedly about skill is a touchy subject, and as we've seen with Dead Space 3, people are hardly happy about being nickel and dimed within a single player experience to the extent one of these companies would want to do. It seems like there is a tendency to want to move into game formats which can be easily monetized in a way people will pay, sandbox games have been doing this pretty well, with relatively bare bones products with half the content shaved off to be sold piecemeal getting away with it. An example being something like "Saint's Row" where they released tons of cars, costumes, weapons, extra missions, a few at a time. I think those kinds of sales are what the industry is looking at right now, especially in a game where they don't have to worry about the expectation of game balance.
I'll also say that politics have gotten involved in the "Modern Shooter" genere a bit too much, and combined with the lack of guts among the gaming industry it's not surprising we're seeing some devs fleeing them like rats from a sinking ship. By being set in the "real world" they by definition wind up making the kinds of value judgements that huge amounts of the population are not comfortable with. Also, without any kind of open war between the major powers who could potentially field serious military forces and hardware against each other, and indeed a lot of trade, you wind up with issues when say China doesn't want to let you sell a game in their country where they are the bad guys. They can't stop people from going off about their human rights record and militance in a general sense, but they can stop you from selling a product in their country, and in general if something is going to get a person there in trouble for saying it, they sure as heck aren't going to let a foreign game take such criticisms to the next level. When it comes to other enemies like say Muslims, we live in a divided nation on the subject as we try and reconcile ideals with reality, you have roughly half the position wanting hardcore crackdowns, and the other side trying to be more tolerant and diplomatic. We have Muslims attack embassies over comedy movie trailers on the internet and murder people, while at the same time we have Marvel comics trying to relaunch iconic character Ms. Marvel as a Muslim to form bridges. Needless to say this causes games where the subject is conflict with Muslims in any context is a focus. Then of course there was that whole fiasco with the "ARMA" team where they got arrested checking out an island they wanted to set their game on, the people there objecting to their island being used as the subject for a war game.
I actually find it kind of amusing when years ago we got complaints about the over saturation of "World War II" shooters and how simplistically black and white they were, with American troops perhaps backed by the Brits and French Resistance fight armies of cartoonishly evil Nazis, where despite the historical setting there is apparently a doom fortress full of chest high walls set in every hillside. The cries "gee, wouldn't it be nice if we had something more modern and perhaps a little more morally grey and ambigious like real life". We see the modern setting shooters arrive, they do well for a while, but then people start QQing about them... after all when the violence is closer to home it now bothers people more, and while grey and ambigious sounded good, listen to the people cry when the black ops guys decide to torture some dude to foil a terrorist plot.... one of those situations where we're pretty much seeing everything people wanted, and after a few years of utter glut, people don't want it anymore, in part because I think they decided they didn't much care for "real life" and "moral grey areas" since in practice it hits too close to home.
Personally I kind of hope the new fad turns out to be FPS games set in pre-revolutionary America where the French and Brits fight it out with muzzle loading firearms governed by realistic black powder physics. Instead of running around knifing each other with customized skills, quick scoping, and setting up ambushes and such while screaming about who is and isn't feeding the other team, multiplayer will consist of players getting together in orderly lines on opposite sides of the field and loading and firing in ranks at each other, breaking rhythm or doing things wrong resulting in an instant kill from a friendly NPC commissar who will shoot you in the back of the head.
The environments can include wonderful scenarios like "Fort Necessity" where under the command of a pre-revolutionary George Washington... gifted with his command because he read three books on the subject... you get to slog through the woods being picked off randomly before building a makeshift fort which he will not clear the woods surrounding the walls from causing ambushers to pick you off again and again without a clear line of fire back at them. After which you can be one of his handful of surviving dudes that will get to sing his praises....
On the French side you will have to master the art of walking without getting your white uniform pants dirty due to your commander being a stickler for such things.
Combined with guns that take like a minute of real time to load between each shot and have bullets that wind up in generally the right place one out of every four times under ideal conditions (and it's never ideal) I'm sure this will all be a new and exciting war experience every CoD player will be scrambling for....