I've run two 5e campaigns at 20th+ and yes it works great. Running Rise of the Runelords currently with level 20+ PCs (they have a bunch of Epic Boons) and it still runs smoothly. Compared to the nightmare of high level 3e or PF, it's fantastic.
Levelling goes fast (particularly after the 6-11 sweet spot). 15-20 go past really quick.
I'd totally recommend doing it. So many DMs rage quit at mid levels and consequence have no experience dealing with high level shenanigans. Accordingly when their next campaign hits mid level and someone pulls a high level shenanigan... they rage quit again.
You've gotta run a few at high level to get used to it.
It's truly epic. IME players love getting a character to high levels, and playing them as epic heroes.
I think there is definitely a certain amount of truth in that. My preference as both a player and DM is lower-key games as I mentioned earlier. I suppose for myself it goes from the level of fun-fantasy (say tier 2 and tier 3) to simply ludicrous superheroic stuff (tier 4 and epic). I've run and played in epic level stuff, but at this point in my life it just seems meh.
The issue is more:
If it is mostly DM-influenced, why is that? and what about it bothers DMs?
Yep, I have never had a GM who was willing to get used to it. So about level 9 - 10 the quite the campaign and reset.
Another thing high level play can teach you (although you can certainly learn it from low level play as well) is not to be so controlling with the game.They then have no experience at high levels. So it just becomes a giant cycle.
My advice is always 'leave them to it, and keep going'. You'll have a few adventures smashed in ways you didnt expect as new powers come online that you had not foreseen (due to lack of experience dealing with as a DM).
The only way to get that experience is to persevere. After a few campaigns through (and past) 20th level, you get a handle on the sorts of things high level PCs can do (simulacrums, etherealness, clone etc) and can plan for them accordingly.
Skimming through this thread makes me wonder if the common unpopularity of high level play is mostly a DM phenomena....
Second, 5E high level characters are insane (IF they get magic items, which unless you're a jerk you're handing out).