The problem is that since most people play infantry roles (assault, medic, etc), more people will be inclined to go sniper (because after all, snipers are anti-infantry units), and the tool traditionally used for beating the sniper (armor) is almost non-existant in a lot of FPS games. The use of the sniper rifle in itself isn't cheap, by any means. In fact, the whole point of the sniper is that they bleed the opponent dry by eliminating their top soldiers, and cause heavy morale losses to the opponent by instilling fear (if you knew you could be targeted any time by a sniper, odds are good you won't be at optimal efficiency). But the way most FPSs are structured right now, the sniper can be considered cheap.
Let's look at the elements of MW2 that make the sniper rifle a genuinely cheap weapon:
1. Thermal scopes. When a squad encounters a sniper in real life, the first thing they do after identifying the sniper's location is to put up a smoke screen, and then advance either to better cover or towards the sniper. Only in COD, the sniper can use a thermal scope to see past smoke screens. To get out of their location, they would have to be running towards the next cover location and expose themselves to the sniper. This is not a successful tactic in real life and definitely isn't successful in gaming. So when the sniper is using a thermal scope, he is extremely likely to get a kill if he pins somebody down or even catches them at long distance even if his element of surprise has been lost.
2. Enclosed environments. This is a natural limitation of video games, but if the sniper is in a corner and cannot be flanked or surrounded, he has a much larger chance at survival when dealing with a standard assault rifle wielding player/s.
3. Lack of armor. This is the biggie, especially on maps where there is little to no cover (Wasteland as an example is a map where snipers can absolutely dominate the game because there is little natural cover to exploit). When you're not in cover, you're a dead man against a sniper. To compensate, we have tanks and APCs in real life; our soldiers simply use them as cover because after all, they're pretty damn close to a wall. But since there is no armor in MW2, you have no way of nullifying the distance advantage a sniper will have over you.
4. Quick scoping. The sniper rifle, as a general rule, is simply too unwieldy to use as a close quarters weapon. They take a while to reload, they're quite heavy and long, and the weapon is not designed to take on more than 1 enemy at a time. But MW2 didn't exactly catch this. The sniper rifle could be used at any range with no loss of effectiveness. This means that even if its distance advantage were nullified, it could still be used in close quarters combat. This is an inherent flaw in a lot of games.
5. Movement. This is a major oversight on a lot of developers minds, that snipers generally don't move when they're firing. It kind of ruins your accuracy in real life, but not so much in MW2. Also, one of the best ways to deal with snipers in real life (artillery) is limited by the fact that after sniping someone or as soon as the strike is announced, the sniper is capable of sprinting out of there, getting away from the strike, then going back once it's over to take up his place again, or moving away and popping someone while the strike is happening.
These complaints can go for a lot of FPS games out there, and are inherent flaws in counter-sniping. The methodology behind the sniper itself is also flawed. In real life, the sniper is used as a tool of efficiency. Assuming the sniper has enough skill, they will most likely get at least 1 kill, but will rarely go much higher. 1 kill is generally enough to instill panic, eliminate any leadership advantage or get rid of a skilled opponent. In video games, snipers are the exact opposite; it's not surprising to get no kills just by being unlucky or not supremely skilled, but if you have the skills, you could get a ton of kills. Player's morales will not falter much with just one kill because it's really insignificant to them, but multiple kills will just make us start raging because we realize we don't have the tools to actually eliminate these snipers.
What could possibly be the solution to all of this? I refer to a few of my real life experiences when I started using a rifle, and one particular campaign mission in COD:MW, when I suggest that tripods might be the key start to balancing out the sniper rifle. Think about it, really the most problematic issue when dealing with a sniper online is that they have free motion reign. If they have a 360 degree view of the area, it'd be hard to flank them because they generally know you're coming, and can target you directly after popping someone else. A tripod will take a short period of time to set up for the sniper, take a short time after being set up to actually remove before the sniper can move again, and limit the directionality of the rifle. In real life, since we're actually only going to aim at just one specific target, we accept these negative aspects of a tripod because the steadiness of the rifle outweighs them. In video gaming, this would be seen as a severe nerf. It eliminates the possibility of using a sniper rifle as a close range weapon (and let's face it, against an assault rifle in close range, the sniper loses 99.8% of the time), eliminates quick scoping, eliminates imbalanced movement, and makes airstrikes semi-effective against snipers. Snipers might actually require strategy to play again, because they would be more confined to specific locations, would need to be patient and would need to scout out the right target, and once they have made a kill, would need to decide between staying put or moving to another location. And in close quarters combat, perhaps the sniper would, heaven forbid, switch to his side arm or use his knife; assuming, of course, he's knowledgable enough to know when somebody is sneaking up on him.
This is kind of making me want to actually try incorporating this into a game like MW, and seeing the end result.