Critical successes and failures can easily exist while still having the impossible be impossible, that’s the DMs job
Player rolls 20 on an intimidation check despite their roleplay being more awkward than intimidating? Critical success, because it’s funny and entertaining usually to do so and it’s theoretically possible anyway.
Player rolls 20 on a strength check to lift a giant iron gate? You did a really good job of trying, but no, you’re not strong enough to lift something 100x your size and weight
Nat 20 on trying to convince the king to give you his throne? He’s amused and either hires you as a jester, or let’s you have a literal replica of his chair.
I see Nat 20’s on skillchecks as “something good happens, but if it’s impossible then the good thing might not be what you expected”
Thats literally not a critical success though. Your example of doing critical successes right is not having critical successes
Not at all. A crit is never doing the impossible, it’s doing the best possible. A crit at first level isn’t going to one shot an elder dragon, but you’ll hit it and do some damage.
A crit trying to lift the castle’s giant, wrought iron portcullis isn’t going to lift it, but it just might help you realize one of the bars isn’t as firmly connected as it ought to be…
A critical success trying to lift the portcullis lifts the portcullis. If it doesn’t, you arent playing with critical successes.
Which is good, because they are dumb
But saying crit successes are fine because they can still fail, with other results? That’s not a crit success.
Flavor the failure to a success then: in an impossible feat of strength, you managed to lift the iron gate high enough for a small creature to crawl through.
Then, depending on how important this situation is for progressing the narrative (whether you as the DM want them to get through or not), you have options to build on their success. Do they have a small creature in their party? Will they be willing to split the party? Do they have the strength to continue holding it up or is there a risk someone would be crushed crawling under? Or maybe their crit success was enough to move it but not enough to hold it at all for a chance for any one to get through.
Thats not a critical success. You are describing a normal DM response to a high roll.
If its a crit success, they succeed in their attempted goal