You seem to be conflating the statements of multiple posters to pull together a Frankenstein's monster of a D&D game.
For instance, the secret compartment behind the dresser drawer than [MENTION=29398]Lanefan[/MENTION] described. This sounds to me like a very fine-grain encounter. The DM has not only identified something hidden in the dresser. They have identified a detailed mechanism for where and how it is hidden, and are prepared for this sort of thing to play out as a prolonged encounter. The players, hopefully, understand the kind of game they are playing, and know that searching a room can require being thorough. I do not imagine that Lanefan is expecting the players to say, "Ok, I've just entered the room with a rug, a bed, a dresser and a mirror. I search the room, looking under the rug, moving the bed, lifting up the mirror, pulling out each dresser drawer and cutting open the back." I imagine that this is meant to be a sequence of actions and investigations. This could just as easily be handled with a sequence of Investigation, Perception and Thieve's Tools skill checks. Any one of those failed checks could mean "no finding the key." This isn't about the action resolution mechanism. It's about the way the DM has set up the adventure and the level of detail with which they'd like to engage that adventure.
I used to create scenarios like the one described above, where searching a random room for random treasure could take 20 minutes or more of game time. Sometimes, I ran them as skill-check heavy encounters, and other times I ran them narratively. These days, I tend not to do that as much — rooms will either have one obviously interesting feature, or character actions will inevitably lead them closer to the target with only a few reasonably well placed actions.
I can't speak to anybody else's game but my own, of course, but the "strategy" that you are referring to is basically one of engaging the fiction. That will be a successful strategy in a game I DM. Paying attention to what the DM says and following up on those things. If, as a DM, I describe a room with 3 features, and, as a player, you ignore those 3 features and just say, "I search the room," you are less likely to achieve your goals than the player who pays attention and says, "Ok, I'm going to check out one of those features." If the player is paying attention, and if the DM is doing a good job at communicating the world to the players, the player will be more likely to attempt successful actions than obviously impossible actions, because the player is not stupid and won't do things that are obviously impossible.
If the players are all having fun detailing exactly how they are disabling or neutralizing a trap using easy to perform actions that do not, individually, have any chance of failure, I'm not going to stop them from doing that. On the other hand, if the players have found a trap, identified its basic mechanism and would like to, "Follow the wires to see how they could be disarmed," I would call for an Investigation check. Which would have a chance of failure. And that's ok. Either way, the game goes on, and hopefully we are all spending time doing what we want to be doing.