Heh. Took a bit of time away to take a deep breath. This was annoying me far more than it should have.
I think this is a part of the issue that isn't being discussed actually. How much swing are we talking about? How does your DM determine DC's? For example, I know that
@Maxperson (in another thread) said that it was a DC 20 to determine 2 facts about a monster and that it was possible that neither fact would be useful to the player in the context of the situation. That that it had to be, but, that it could be.
I would not do this.
To me, I look to the bounded accuracy of 5e. How many monsters have an AC over 20 for example? Not very many. Most of them are pretty legendary encounters. So, I apply that to the skill system as well. Any DC of 20 or higher is something of legend - this is something that even a highly trained expert will fail most of the time, so, it's pretty darn hard and it's something you'll likely only see a couple of times in a given adventure. Over 20? Couple of times in a campaign. The vast majority of checks, in my view, are between DC 5 and 15.
Which means that now, asking for checks,isn't anywhere near as swingy as it might be supposed. For an unskilled character, an easy check succeeds about 2 out of 3 times. For a skilled character, that becomes a Moderate (15) skill check.
So, to answer the original question of the thread, "Why do you want to roll a d20?" Well, I know that if I roll, barring unforseen complications, I'm going to succeed about twice as often as I fail and I can spend character resources to improve those odds even more. So, why shouldn't I roll? I'm losing out on those character resources if I don't roll and rolling will get me what I want most of the time.