Using Skills versus Declaring Actions
The reason I think the distinction is important is that if you start allowing players to just state, "I make an X check" you are essentially training them to stop thinking. Why put the clues together and realize you should look under the drawer when you know you can just make a skill check? And if the DM knows the players are just going to make a skill check, why put the work into creating the clues?
Summary
While Hussar's play style is legal & valid, I think it's leaving a lot of fun & interesting gaming on the table. It's qualitatively if not quantitatively the same as rolling Investigation from the tavern instead of first going to the office. Yes, it does take more DM prep to do it iserith's way, and if that work isn't done then, yeah, all this stuff is "just the boring part before you get to fight something."
I've had DMs that wanted me to describe how I searched a door for traps. How the frick would I know? I'm not a rogue. I'm not trained in finding traps. Besides if I describe how I carefully sprinkle talcum powder or use a small mirror on a stick to check that spot I can't quite see is
it's boring. Not only to me, but to everyone else at the table.
Sometimes traps are more than just traps. It's a puzzle you have to figure out (although I pretty much hate puzzles/riddles in most games as well). Sometimes searching the office should be more than just searching the office. For me, most of the time it's just either "you only have a moment to search" in which case they probably wouldn't find the note taped under the drawer unless they rolled extremely high or "the guards are nowhere in sight, do you want to take your time?" In that case I may not even require a search check, or have them make one just to see how long it takes. Sometimes I'll ask something along the lines of whether they're being careful to not leave a trace that they searched the room.
I would no more ask a player to describe how they are searching the room than I would ask them how they are cooking dinner. Unless of course they (and the group) enjoy that kind of thing.
As far as "training them to stop thinking", I simply disagree. I'm simply not forcing them to play "my way". Sometimes interacting with the environment can be enjoyable, but most of the time it just feels like filler that does nothing to advance the story. Frequently filler that only engages one person. It has nothing to do with being a lazy DM, but the reality is that my time, and the group's play time, is limited. I'd rather spend my time figuring out that the captain of the guard is really the baron's cousin and they've been conspiring together to steal from the merchants who have become more powerful while framing a political dissident and how to drop bread crumbs for the group to follow if they want.
When the player does an insight check it prompts me to think of a way to reward that initiative by uncovering something up with some subtle clue. Maybe the guard is a bit nervous and glances in the direction the captain just came from. Maybe I would have thought to do that without the request for the skill check, maybe not.
For me, I just think describing your actions by asking to do a skill check is a perfectly fine shortcut the majority of the time. When it's not, I'll prompt for details.
As far as what's fun, different people have different preferences. When I judged for public games, my tables were always one of the first to fill up. My games are very heavy RP and I've had people put up with me as a DM for years on end. My style is just different than yours.