It's the "automatic" part that bothers me, as so many things aren't automatic at all.
Even if things are not automatic in the real world (but are they really not automatic ?), it does not mean that they need to be manual in their resolution, because it's only a game. I suspect (seeing as you employ the world "realism" below), that this is a fundamental difference in our approaches.
My take is that D&D certainly does not aim at realism. It's intent is at best simulationist, but with a simulation of the high fantasy genre, where it can be as narrativist as really simulationist. It's a matter of taste.
Using the "search the room" example, if I hide somethine really well in a room - say, in a very-hard-to-detect secret compartment in the floor - and I send 100 different people (or groups) in to search for it, even if they have all day the odds of all 100 groups coming out having found it are negligible. Ideally, if my hiding job is good enough none of them find it; but it's inevitable some will just by fluke and some others will by either skill or deduction or whatever.
But this is not the principle of Take 20. The principle is that the group dismantles the room and takes as much time as needed to find whatever can be found with their skill.
If you do the exercise above in limited time, I agree that luck is important (what are you searching first ?), but the principle of Take 20 is different, you have given all you can, so narratively it makes sense to skip to the conclusion.
Again, a matter of taste, I understand your realism perspective but mine is different in a game which is about storytelling (mine is, at least).
I'm not after story-driven, though, in that sense; nor am I all that concerned about speeding up play by skipping over details (some here seem to want to sacrifice half the game on the altar of speed). I'd rather see the story emerge from the detailed run of play.
If this is what your table is looking for, it's perfect, it's just that there are so many ways to play the game.
Problem is, this allows players to meta-game their characters into always just happening to have exactly what they need when they need it; which means that anyone who bothers to put the forethought into equipping their character properly ahead of time is wasting their time, and also means some challenges might be easier to overcome than they should be - or even outright negated.
If some players indeed take the time to fill in their character sheet, I understand them feeling a bit cheated if this rule is used. But then, it's a question of preference at the table. If everyone prefers a more inventive game (this is not to say superior) than one rewarding preparedness (which is also a quality), it will not be a problem and even analytic people will enjoy the end result, I think.
Never mind that even mundane gear costs money, and particularly at low levels not every character can afford a complete kit.
This is why for me exploration with that level of detail is reserved to the very low levels, in which case it works OK.
Yes it's about role-playing - we agree there! But sometimes that role-playing is going to include "Damn, I forgot to bring that." or "Damn, I wanted to pick one of those up last time in town but couldn't afford it!"
And I'm fine with that, but it's a question of context. This is funny when you're looking for a string to hook the kobold trap, but when assaulting the astral fortress of the Lich Queen, it's not going to hand on a piece of string.
I mean, it could in a sense, but players will have myriad of other solutions at that point in their career.