The swingy 1d20 is not particularly good for adjudicating anything honestly. That this specific die has become “the one die to rule them all” since 3E isn’t something I can pin down on 5E specifically, but it didn’t reject it either.
I get some of it, it’s a simple concept. It streamlines play if all chance is based around a single mechanic. Adding the advantage/disadvantage helps tremendously, but it still doesn’t work all the time, and the mechanic starts to make itself become overly important in character builds as well.
If you wanted to build a flatter spread, something like 5d4 for proficient actions, dropping a d4 every 4 levels and just add +4 to the roll seems like a better way to adjudicate probability without have to create unattainable DCs as challenge ratings increase. Instead of a +/-1, you add or drop a d4 from your roll?
I do totally get the combat slog of 5E and it’s definitely the result of hp bloat. That AD&D/5E fighter & ogre example was extremely good at showing just much different it is in that regard. I’ll add that morale ratings should never have been removed after 2E either. Unless you’re fighting undead, extra planar fiends or elementals, or a dragon, it was pretty rare for a fight to slog through to the last NPC hp. Granted, it’s always been DMs prerogative to determine if the NPCs will break and flee, but pre-3E it was a built-in stat that implied how willing Jimbo the Ogre was to lay his life on the line.