OK, I'll start by stating something very emphatically:
I have no mods. None, nada, zilch, zip. I've never run mods on Skyrim, so please get that out of your head.
Second: This is a brand new install of the Special Edition. I also have the original Skyrim loaded in a completely different directory with a completely different save folder. There should be no cross-contamination. The Original Skyrim does not have the problem below.
Mild spoilers ahead. If you've never played the game, then it's a spoiler. If you have, it isn't because it literally happens in the first 10 minutes of play.
Now on to the problem: When I get to the point of my head being on the chopping block, the headsman decides to be undecided. He sits there swaying along to his internal music (I think He's a Bieiber fan) and Alduin must hate Bieber, because he never shows. He doesn't fly around or anything. He just refuses to show up. And apparently the headsman is so enraptured by his music that he won't lift his axe to behead me. By the way, this is the only time in the game where I side with Alduin at all.
I've tried the following:
3 new game starts. 2 with an Argonian, one with a Khajit.
Deleted the Skyrim.ini and the Skyrimprefs.ini from the Skyrim Special Edition folder in my Games.
Letting the headsman sit there on screen while I went to lunch. Nope... still grooving to a useless Canadian named Justin. (Note: Most Canadians aren't useless. They're actually very nice people as a whole. Don't let Bieber sour you on Canadians. In fact, go visit Montreal, Toronto, or Vancouver some time. It's a great vacation... in summer)
So does anyone have any idea other than completely nuking the game from orbit? I hope that's not the only way to be sure because It's kind of a PITA.
TL;DR Just say no to Justin Bieber. It's what's best for all of us.
P.S. Did I mention that I have no Mods loaded?