You should at least have a general idea of your PC's skillsets. As in, don't let the country bumpkin make Arcana checks about monsters he's never seen, or let the stick figure try to punch down a wall. If you look at a character in a situation and think, "there's no way that could succeed," then they shouldn't be making a check.

"No" needs to be said before the roll, IMO. Then If the player insists on doing something impossible anyway, just role-play the failure. With that said, actions that are in a narrow sense impossible can still have positive outcomes and if there's the potential for that then I'd say roll for it. The proverbial dragon seduction attempt can still flatter a dragon with a big ego enough to benefit the PC even if it doesn't get the PC laid.

They do if the DM says they do, y'all get way too hard for the rules as written.

...If we fall off the rope bridge because you did a backflip I'm haunting you though.

In addition to what the others have said, I think degrees of failure are often a fun thing to introduce whether they are in the rules or not (I'll assume D&D 5E). It might be that a 20 with your +3 athletics isn't enough to completely leap over that huge gap, but you manage to grab a handhold a few metres below the edge. The cleric's roll of 3 with a -1 athletics, on the other hand, sees him plummeting to the bottom and taking a heap of fall damage

They do at my table. Because it's more fun, god damn it!

I have zero regrets about my sick-ass backflip.

Why the hell not? You're the DM. Why do you not have copies of your players character sheets?

D&D is that way, though. Every time you see a natural 20 for anything that isn't an attack does not automatically succeed unless people are using homegrown, which they often are.

I think we're talking past each other here-- everyone is saying it SHOULD be a rule and everyone they know does it anyway so it's "part of DND". It's like stacking +4 cards in uno. Might not be in the rules, but everyone knows to do it.

2 things: 1: I've gotten disco Elysium, and Ive only played a few minutes, but I don't remember it having rolls like that? How does one know what one is rolling? I played like 20 minutes of it 3 months ago, so maybe I'm misremembering. 2: that's how my brother DMs. I once critfailed a lock picking so badly that my character broke his finger. My brother laughed his ass off

A lot of dialogue points and other actions will bring up a thing that rolls 2 D6s. Snake eyes is a critical failure, double sixes is critical success. The earliest point in the game where you can make one of these rolls is in your hotel room. Either by attempting to get your tie out of the ceiling fan, or by using the mirror and trying to stop making "The Expression." Many of them can be re-rolled later once you get more skill points. Others are one and done unless you reload or start a new game.

Not to mention which game you're actually playing.

I regularly play in groups with eight player characters, Kolkani. Do you want me to check all eight of their sheets and all their abilities that could possibly modify their scores or just ask them to make a Blah (Foo) check check and see what the result is? It's gonna be way faster for everyone to just ask them to roll.

Having that 1 player being stalked by a horny dragon for the rest of the game, just in case.

How do you create fair encounters without knowing your player's character's stats? 🤨

Think of it from their point of view though. They want to try and do something. For me to just flat out tell them "no, there's no possible way" is discouraging and robs them of autonomy. Obviously for crazy extreme circumstances I won't let them, like "let me convince the king to abdicate to me!" type things. But if I think the DC should be 25 or something I'm not gonna bother wasting my time calculating what the theoretical maximum could be for the roll because I genuinely cannot know. The player can always do things I don't expect or use other players' things to help. For reasonable but implausible things I'll allow rolls even if a nat 20 wouldn't work because I'm not calculating what a nat 20 could theoretically be. Plus, I often give people little flavor benefits for nat 20s even if they don't have mechanical success.

Throwing whatever you please at them. It's fair because they're informed of the risks and given opportunities to adjust their plans.

20 peasants stand on the edge of the Grand Canyon and attempt to jump across. On average, should one succeed?

In casual play you can rely on veteran players to know their stats. If they're the type to lie intentionally then they can leave the table. If they're making mistakes then maybe something goes a little too easily, oh well. The best DMs i had didn't give a shit and focused on rewarding players for learning.