In our fourth edition game, our party's rogue has gained the habit of checking for traps whenever he moves anywhere.
I find this annoying, not only because it stops traps from ever coming into effect, but also he does it whilst he's talking with other characters. While talking with the evil wizard right before the boss fight, which really ruins the atmosphere.
Other players are also annoyed by this as the character is already optimized and so is the best in combat by a long shot. He doesn't need this moment to shine.
Best Answer
Checking for traps in combat does cost action economy
This is important to keep in mind as there are quite a few minor action attacks that strikers get access to as they level and looking for traps is also costing him possible damage.
Out of Combat I would rule that searching precludes any other activities
The PC cant be actively searching for traps while carrying on conversations, etc. Passive Perception handles the normal awareness level of a PC while they move and do other things.
Talk to the player OOC
Express the issues you and the rest of the table are having. I can easily guess the having to adjudicate his search roles all the time just brings the game to a very slow grind. Maybe even make a social agreement about telegraphing whether or not traps might be in a certain area as a way to preclude the player searching all the time.