And the PCs should be automatically suspicious of statues because it's on the checklist of things to be wary about, right?
There are two reasons why the PCs should be automatically suspicious:
1) They're experienced players, and they're meta-gaming. They expect that the DM will try to catch them off-guard, and that it's their job as players to be as paranoid as possible.
2) A player is playing a character who is an experienced adventurer, and the character is prone to paranoia as a personality quirk.
Constant vigilance! It's not paranoia if they really are out to get you!
Of these two possibilities, the first one is the player's fault. Players shouldn't act on knowledge that their characters don't have, and the DM should point this out if they forget. The second option can be fun, but there's no reason why it should take up an inordinate amount of time to narrate that the character performs the standard set of trap detection techniques and finds nothing.
The only time where it might really be an issue is if the characters have an in-game reason to suspect something, and the outcome of a standard search technique is uncertain because there actually
is something hidden without any clues to indicate it. If the characters have encountered gargoyles (or piercers, or mimics, etc) in the past, so they're always on the lookout in the future,
and there are more gargoyles/piercers/mimics that they might find again if they remain paranoid about it.
The obvious solution, then, is for the DM to not re-use the same gimmick and expect it to work again. Once the players know what to look for, there's no point in that monster ever showing up again, because it
isn't going to surprise anyone. And if that monster
does have reason to show up again, the DM can cut to the chase and just tell the players about it outright, since it is knowledge that their characters would be able to figure out.
"The ceiling of this cavern is beyond the reach of your light; based on past experiences, you know that you're in danger from piercers."