I agree, constantly telling the DM I'm checking for traps to avoid gotchas does sound boring. I'm glad we agree. It doesn't happen in my game, either. Did you think it did?General approach is something we discuss. What does the slow and cautious approach mean both in terms of time and effort. What the standard "default" approach is, clarify that even passive checks will be at disadvantage if they're rushing. I may go into more detail the first time or two for different environments, but it doesn't take long to establish a standard baseline.
So we, as a group, make that decision once and if there's ever any question or uncertainty about how the PC would approach the situation I ask for clarification. Same as any other skill based challenge. Like I said, I find constantly having to remind the DM that I'm checking for traps (much less specifically how I'm checking) to be boring. As I've said before if the player suspects something might be trapped, I assume their PC is suspicious and will take precautions whether or not there is a trap. If that includes a dice roll, I don't see why that would cause the world I've built to crumble it just means the PC acted on their suspicion.
I play the game to slay dragons, win the damsel's heart and get shiny bling. I'd simply rather spend my time on social interactions, discussing clues, fighting monsters than describing how I search a room so I'm sure to mention that I search under the mattress.
I also play for the same reasons and find all of my play centers on interesting encounters driving thise goals. Did I say something to make you think otherwise?
I ask these questions because instead of engaging the clear examples I provided of play at my table, you seem to rather say that you play differently and then list ways our game are the same in terms of playgoals and interests. Yet, your issue is about play style, not play goals. So, I remain confused as to why you keep asking how I and others play, but then when shown pivot to complaints about things that aren't happening at our tables and ignore the examples of play.