The door doesn't get to try to force you open in return, unless it's a mimic.
I'm not sure I understand why there's a difference. I mean, I get that you feel that there's a difference, and that you're not alone in thinking that.
To my mind, trying to climb a cliff when there's a risk of falling isn't much different than attacking someone who can hit you back if you fail to defeat them. There's a consequence for failure.
But combat is typically resolved with many rolls, and nobody thinks anything of it that some rolls fail. You keep at it or you die.
Then suddenly, with an ability check, you do get the "no, sorry, can't try again". Back in my AD&D days, I never gave this much thought. I was told that if I failed a Thieving skill check, I couldn't do it again until I leveled up. Fail a spell learn check? Get more Int.
Fail a Bend Bars/Lift Gates or an Open Doors check? Usually the same.
It wasn't until later, when I started playing characters with more Non-Weapon Proficiencies (and later skills) that I started to considering something was strange with that mindset. It makes sense for a computer game, but as most of the people I gamed with started caring more about "verisimilitude" and "the game making sense" (as dubious as that can be sometimes), I started pointing out that this sort of thing doesn't make much sense either.
"You fail to find the book you're looking for in the library." The DM said.
"Can I keep looking?"
"No, you just can't find it."
"Unless it's not there, I'll find it eventually, right?" I replied.
And I got pushback for asking these kinds of questions. Again, people do think there's a difference, but I don't really grok what that is.
I had some friends who were into LARP (I don't recall which one), and they would explain that, in the LARP they were part of, if you test an ability against a player or NPC, and failed, you weren't allowed to try again- it was now a known fact that they were better than you. So if you tried to punch a guy and he dodged, he'd continue to dodge every punch. So you had to switch to a weapon or give up.
I didn't quite get that either, since it eliminated luck, but then again, that's a diceless sort of game.
Sports teams have spent a lot of money on research as to why players perform better some days than others. Why the same batter, against the same pitcher, on the same field, can be "on fire" one game, but mediocre the next.
What people keep pointing out to me is that a skill check might not be one swing at bat. It might be three. Or an entire inning. Or an entire game. Or an entire series. And that on a long enough timeline, the results of a d20 will eventually end up average.
But it's not like passive scores are used in games like that. If I make a downtime check for something that happens over the course of a week, it could be one roll of a d20. Then the next time, even if nothing changes, well, the result can be wildly different.
A lot of DM's hated it during the 3.x/PF1e days when you could take 20. They felt you should always roll. They'd often deny you the opportunity (IME) not by stressing how long it took, but by saying "well, something can happen if you fail". Because that's all take 20 was modeling. It was a shortcut for retrying again and again until you got it right.
Because if you search a room, one would hope you eventually find what you're looking for (granted, I have met some oblivious people, but not being able to make the check in the first place, or not being able to take 20x as long is a real possibility sometimes).
And today, well, there have been a lot of arguments about passive Perception (as an example) and that it should never be invoked. It's not a floor, and you can't just walk around and expect to passively seen hidden things, even if your passive is through the roof (the arcane gyrations made to prevent Observant from doing anything useful that I've seen are wonders to behold).
Heck, when I pointed out that advantage/disadvantage raises and lowers passives, I remember being told (by people who had played 5e a lot longer than I had at that point) that I was smoking something, despite it being right in the PHB!
I can see that people want high stakes on rolls. They want the non-combat part of the game* to be pretty much pass/fail and move on. I just don't see why. Especially when most of the rolls that are being asked to make seem a bit pointless.
DC's are often inflated to the point that you'd have to be a Rogue with Expertise to hit them, checks can be proficiency gated, DM's will rule that you can't be Helped, they'll grumble about Guidance, but when the high level Fighter sneers at AC 19, well, that's just how the game is.
*Unless you can make an ability check in combat routinely. Like 2014 Grapple. Surely nobody would say that, having failed to Grapple someone once, you couldn't try again? Or free yourself from one?