Unless the Z's are really bearing down, it's pretty easy for just about every player to search once per turn. That seems too...easy. Or is the idea to turn and burn as many cards as possible to get to the good stuff? In that case, why even bother with the fluff items?
Maybe I'm thinking of Descent too much.
I think that's an intended part of the design.
In my games of Zombicide Modern, I've trimmed a lot of "fluff" items, just to speed up play.
Keep in mind, that's a difficulty adjustment in the player's favor.