It's clear from the 1e DMG that Gary Gygax didn't want a cautious play style.
Assume that your players are continually wasting time (thus making the so-called adventure drag out into a boring session of dice rolling and delay) if they are checking endlessly for traps and listening at every door. If this persists, despite the obvious displeasure you express, the requirement that helmets be doffed and mail coifs removed to listen at a door, and then be carefully replaced, the warnings about ear seekers, and frequent checking for wandering monsters (q.v.), then you will have to take more direct part in things. Mocking their over-cautious behavior as near cowardice, rolling huge handfuls of dice and then telling them the results are negative, and statements to the effect that: “You detect nothing, and nothing has detected YOU so far —“, might suffice. If the problem should continue, then rooms full with silent monsters will turn the tide, but that is the stuff of later adventures.
And yet most of the rest of the text encourages just such a style.