I echo many of the sentiments here. Close-quarters combat can be hectic and stressful, trying to turn around as foes move behind / around you, catching up to them as they run, etc.
Not sure, exactly, how Skyrim did it differently but there I rarely had a problem sneaking up on foes and skewering them with a dagger without alerting their buddies. Perhaps it was the large number of dungeons and such that made that tactic easier? Sneaking up on someone out in the open is extremely hard in Fallout-3 (been practicing recently).
The main appeal of sniping, to me, is that you control the fight. You decide when the fighting starts, and -- oftentimes --- you also determine when it ends (after your one shot ). Sniping has the further advantage that ~usually~ you are far away from melee range and sometimes so far away that even if other foes are alerted they can't pinpoint you before you can snipe more (or move).
The down side of sniping is, of course, close quarters and being surprised. The one time I played a multiplayer game with my brother and some friends, I quickly snuck to the second story of a building and started sniping them. Unfortunately, being un-used to fighting respawning ~player~ foes, I didn't realize they would figure out where I was.... imagine my surprise when I'm staring down the scope, looking for targets, only to hear a loud boom, turn and see my brother with a shotgun to my face (how he missed the first time, I do not know).... with a sniper rifle equipped, I ~tried~ to shoot back, but at that close range it was too easy to miss, and reload takes forever (normally not an issue).
So sniping definitely has its place and its own method of play... but there are times it simply does not work well. That can be said of other weapons ./ styles of fighting, too, though. Rock-paper-scissors kind of thing ---- an expert martial artist is not going to be too effective against a sniper stationed at extreme rifle range and up high inside a building, sniping at the martial artist who is standing in an open field, for example. Turn the tables and put the martial artist ~in~ the building with the sniper who is stationary at the window as the martial artist sneaks up on him, though.....