Except that in real life if I fail to break the door down, I can try again. Which I probably will, especially if I’ve broken down identical doors before.
Right, which is why we roll the die. A person’s assessment of their own abilities is not 100% accurate and they can’t account for all possible variables, so the dice make a decent abstract representation of those unpredictable factors. Which is all well and good, as long as there is something stopping the character from trying repeatedly until those unpredictable variables line up just right. Which to be fair, there should be most of the time; at bare minimum, the time it takes to perform the action should ideally bring you that much closer to the next random encounter. But some DMs don’t put in the work to make repeated attempts costly, and instead just rely on meta-game costs such as artificially limiting the number of attempts or artificially penalizing repeat attempts. And that breaks my immersion.
Take 20 is dumb. It’s an attempt to mechanize something that should be a DM judgment call so as to make it player-facing, and it’s a mess. I’m not advocating for take 20. The better alternative, in my opinion, is to structure your adventures such that most if not all actions have meaningful costs or consequences (ticking clocks and/or random encounter rolls at fixed time intervals go a LONG way here), and in the odd case that there is nothing stopping the player from retrying forever, just montage over the time they take trying and retrying.