The problem (referring to the above something that only x can do) with this is that you can easily end up with circumstances that negatively impact the game, all for the sake of niche protection.
A prime example of this was 3.x rogue Trapfinding (which, IIRC, stated that only classes with trapfinding could find traps with a DC 20 or higher- most traps). Your character could be a master trap maker with a +50 search check, but unless you took a level of rogue (or one of the few other classes with Trapfinding) you could locate only the crudest of traps. It neither made sense nor benefited the game (IMO).
It was problematic because if you didn't have a trapfinder in the party, traps became that much more deadly (most DMs I knew simply would avoid using them without a trapfinder, because we weren't the biggest "Gotcha!" fans).
I think that a better approach would be to accentuate something that a particular class excels at. For example, rather than declaring that only rogues can find traps I think it would be better for the game as a whole to simply give them a bonus to finding traps. Of course, the pitfall of this is that it can easily lead back into the situation where either the rogue is the only one who can find the trap (because the DC is adjusted for a rogue with trapfinding) or the rogue automatically succeeds at trapfinding even when blindfolded (the DCs are calibrated so that anyone has a chance for success).
One solution might be to offer the rogue a small bonus (such as a +2 which doesn't much unbalance the DCs), or a feature that guarantees he's one of the characters with the highest trapfinding ability (such as allowing him to use his highest ability score in place of Wisdom when searching for traps) to reflect his expertise, but I imagine most would consider this insufficient differentiation.
Funny you mention trapfinding; out of all the games I've played recently, this is one of the areas 4e botched when it came to "improving" on 3e.
The best trapfinder in the game is not a rogue; its a druid. The Druid is wisdom-prime AND has perception on his class list. Tack on a +2 wis race and/or a race with +2 perception (hello elf) and you have a trapfinder that can't be beat (extra cheese: throw on a background with a +2 perception boon).
A rogue can't compete with that. Wisdom is a dump-stat for rogues (since it shares a load with charisma, which is infinitely more useful to all rogues, even brutals) and rogues get no bonus specifically to searching traps out.
After 3 games with a minotaur druid and a human rogue, trapfinding became "Minotaur, do you see any traps I need to disable?"
I'll give you two examples on how trapfinding could have been better handled without resorting to "you must have this class ability to find traps".
Pathfinder: Anyone can use perception to find mechanical traps. Only rogues can find magical traps without resorting to spells. In addition, a rogue gets a bonus equal to 1/2 their level to find traps of any type, insuring they'll always have a higher bonus than another class with a similar rank in perception.
Basic Fantasy: All classes can find traps 16% of the time (1 on 1d6). Thieves get the ability to find/remove traps (which begins at 15% on a d100) but increases with level, so that a 2nd level thief has 20%, a 3rd level 25%, etc. So while a fighter and a thief have roughly the same chance to find traps at 1st level (16%, +/- 1 pt), a 10th level thief has a 55% chance, while the fighter still only has 1 in 6.
Both allow non-rogues/thief to search for traps, but maintain niche protection for the rogue/thief to be better at trapfinding. Ironically, 4e doesn't provide said niche protection to rogues, and thus rogues make worse trapfinders than any other class with a high-wisdom and perception training.