Personally I think the whole issue is the really poor method we have for searching for stuff.

In tabletop, usually I ask, can I search the room and either the DM narrates what we find or ask for some roll like investigation to determine how well it was searched and what we find. Never have I had to search a box, search another box, search that dresser, etc.

Same thing with bodies, I ask after a combat to search the bodies and that happens to a group of them, I don't have to roleplay going through each individual body.

My suggestion would be drop all containers that have nothing and add a passive investigation check like they been doing for perception checks. If you detect something, that container has a soft yellow glow about it.

This would let you search rooms quickly.