as DM, I was very aware of the fact that the happy result was almost pure coincidence and would almost never happen. I'm pretty sure the players wouldn't have been happy if I'd just said, "Nope, he's slightly stronger than you, you lose, have a nice quest." But 5E doesn't really support any other resolution mechanisms either
There's roll d20 vs DC, of course, that's it. But, there's a number of ways to use that (shy of inventing your own).
le'see, dramaticized arm-wrestling could include:
Intimidate Check to 'psych out' your opponent
STR check to beat him quickly
CON check to wear him out as you struggle
Bluff check to feign weakening so he makes a final push while you're still able to handle it.
STR check to put it to bed.
By spreading it out over 5 checks, you can even out the swinginess of an opposed check, and ratchet up some drama.
OK, in a sense that's a complexity 1 skill challenge for a single character, or 3e 'complex skill check,' just using different skills, but whatever. It's shy of making up your own resolution systems, it's just applying the d20 resolution system in more detail.
I'm still evaluating what 5E and AD&D each bring to the table. So far it seems to me that 5E has more exciting combat but AD&D has better pacing.
Better pacing? You mean because 5e lets a long rest re-set just about everything very simply, rather than resting so many hours to memorize such level spells, then 15 or 10 minutes/spell level to actually memorize them - or, alternately, if none of you are casters, up to 6 weeks to get all your hps back?
One question is, is it easier to fix 5E's pacing or AD&D's combat dynamics?
It might be easier to talk your players into GURPS.
5E's pacing is baked pretty deeply into the system-- ... to rewrite all of the 5E classes that are oriented around an "adventuring day" as the unit of play.
5e is vaguely balanced around this semi-mythical 6-8 encounter / 2-3 short-rest 'day' (24 hr period in which you are allowed one long rest). Were it not for the short rest mechanic, that would just be a simplification of AD&D's complicated system of memorization and mostly-superfluous coverage of natural healing too slow to matter, that mostly just (IMyouthfulX) boiled down to ' we're outta spells & low on hps, - we go back to town and rest.'
I can see the dissatisfaction with the former, but not so much the appeal of the latter as a 'better pacing' alternative.