One thing that seems to be missing in this conversation is the planned rolls. The ones DM's write into their adventure. I know for me, I write in all the skill checks that can alter an important scene, plot point or character arc.
For example, characters taking a rowboat to shore in rough seas. A flipped rowboat could mean the paladin has to take off his armor and leave it on the bottom of the sea. That's a serious consequence. So that roll is written in very specifically. The DC varies based off the players' judgement. Characters that grab bails, grab an extra oar, etc. things they may come up with on their own gives them a lower DC. I write that stuff in too.
Point is that many of the circumstances we are discussing, DM's plan for. Hell, I even write DC's for persuasion based on how they approach the NPC needing to be persuaded. Some people like to be sugar-talked others need to be intimidated, and still others need to have an honest forthcoming approach.