My friend feels very strongly about this. I'm less vehement but certainly agree that many games are immeasurably improved for their absence.
I was interested to hear others thoughts. I guess I should add that this is specifically about their impact on others rather than their experience to play.
TF2: The Sniper and Spy are broadly lone wolf classes (or at least that's how they're commonly played) in a game which ostensibly encourages teamplay. Dying to them often feels like you were cheated (particularly spy) as kills by them are often abrupt and you will feel there was little you could do differently to avoid death.
The counter to this is that they're obviously very situational, so if you hadn't popped out from behind that corner you wouldn't have gotten shot. Likewise if you'd had a pyro constantly spy-checking then the spy stands no chance. However is this actually part of the problem? Their presence forces others to act considerably differently thereby constraining their gaming experience and thus limiting their enjoyment (e.g. having to cower behind the corner or perhaps switch class).
A counter argument says you may as well moan about "oh well its BS I couldn't walk over that Demoman's mines or waltz past that Engineer's sentry", and its a valid point but for some reason they feel different in a way I can't quite define. I think it comes back to the abrupt finality of Snipers and Spys. When killed by them at the end of a nice streak rarely do I feel "nice one, good shot...you bastard" while I might if killed by a Soldier. My deaths to them aren't learning experiences but rather annoyances along the lines of "Oh wow, you totally know how to click a mouse button....thanks". There feels little skill involved in sniping someone, which is a little harsh I know, but that's the way it feels.
I think part of the problem is perhaps the lack of consequences. While all classes throw their lives away to some extent (especially pyros) I take great annoyance from a Spy who's willing to sneak behind our lines and then stab me in the back in full sight of my team knowing full well he'll not get 2 yards before being gunned down.
WoW: I could cite a whole other bunch of FPSs but instead I'll give a bit of a contrast with WoW and the Rogue. Firstly though I should preface this by saying I've not played WoW since before Cataclysm so can't comment on their current state. I should also add that I think the 'issue' is considerably less in the like of WoW vs TF2 but its certainly still present.
I can remember battlegrounds where you'd be pottering along only to suddenly get stunlocked by an invisible enemy who proceeded to insta-kill you. Now obviously you had things like a trinket you could use to get out of the stun lock but if that was on cooldown you were stuffed.
Again I think it comes back to the issue of not really learning a great deal other than oh, so I guess I should never let my trinket be on cooldown...