>I'm pretty sure most people have a pretty intuitive understanding of how to perform a methodical search of a room
And surgeons were pretty sure they'd never leave an implement inside a patient, but the stats still improved with the introduction of checklists. Like checklists, the quadrant method means there's less demand on your memory, which means less chance of forgetting things if something unexpected happens.
The checklist can also be ordered such that the lowest-hanging fruit is covered first. Start with the vent covers, overhead lights, and smoke detectors, because those are the places where it's easiest for an unskilled spy to hide monitoring devices. Any hole cut into the sheetrock for a legit purpose could also have a peephole near it.
I bought a house that had a slight dimple in the heating duct of a ground-level bathroom, mostly concealed by the vent cover. I went down into the basement, and surely enough, from a certain spot, I had a clear view of the toilet and shower from below. I bent the duct back flush with the edge of the hole, and concluded that was probably one of the reasons that the sellers were getting divorced. So you might not find a camera. There might be an actual eyeball there sometimes. An electronic scanner isn't going to find that.
And surgeons were pretty sure they'd never leave an implement inside a patient, but the stats still improved with the introduction of checklists. Like checklists, the quadrant method means there's less demand on your memory, which means less chance of forgetting things if something unexpected happens.