What sort of game are you playing? If it's a classic dungeon crawl, then the odds are pretty high.
If it's a classic dungeon crawl (which is a niche itself), then the players are probably moving slowly and searching everything, so the elf ability is unlikely to come into play. Even if you have an elf in the party, he doesn't get a search check to notice other things (like traps), so the party should still be searching. As in this example:
Player: (Thinking there's a secret door nearby) Do I, as an elf, notice a secret door?
DM: If you did I would have told you. (In that he already made a secret roll - or not, if there is nothing to be found.)
Player: Okay, let's spend a turn searching this area.
Here, the player rolled a Search anyway. AFAICT, the free check he was entitled to affected the order in which events were narrated, but not the actual outcome. If there was a door and the player beat the DC, he would have found it, otherwise not.
The elf ability only matters when there is a secret door and no one is looking for it. It could come into play if the characters are in some non-dungeon building and there is a genuinely secret door that no one expects, or if they're in a hurry for some reason and don't have time to search every inch of wherever they are.
Moreover, the thing with secret doors is that in general, it's in a DM's interest for the player to find things that he takes the time to create, so if he does take the trouble to create one, he probably will let the players find it one way or another. That might not be the case if we're assuming an antagonistic DM who is genuinely testing the players to see if they can find things. Which again is fine but is not what everyone does.
And, of course, there's a first level spell that finds secret doors without a check. If you're expecting them, that's probably going to override the whole elf thing.
LostSoul said:
That's what a DM is, definitionally. See the "final arbiter" text or various other examples that are posted elsewhere in this thread.
Or rather: In what way does it best serve the game?
A lot of ways. For one, an individual DM knows what is going on in his game better than the writers of the game do.
Such as whether there are likely to be secret doors in his game, how he is interpreting the search rules, what the temperaments of the players are, whether he wants to play the game in such a way to make these elements matter, and so on. So deciding how specific permutations of the perception rules work is a perfectly rational exercise of his discretion.
Another benefit of having the DM control the rules is it makes the game run faster. If the conditions described above are not true, and the elf ability is not going to be relevant, it's a waste of time to think about it, and a wise reason to let it go.