I did not enjoy Shadowbringer (SPOILERS)

[ProstheticSoul]

"It was deliberately written so the story makes sense with or without completing the Crystal Tower story line"

I deny this assertion with every fiber of my being. Flat out false. Full stop. I just checked my cut scene history, and apparently I had already beaten the Crystal Tower raids. However, let me be brutally candid here--Shadowbringer on the whole dd not make a lick of sense to me anyway, especially concerning the parts involving the Exarch. And if a player hadn't even touched the Crystal Tower sections beforehand the story would have had ZERO emotional weight. Not less--ZERO. Nada, nothing!

As an aside, turns out I did memory hole the entire Crystal Tower saga. That must been one of the sections I completed before the seven-year hiatus. And that would certainly go a long a way to explaining why the big hood reveal amounted to jack and squat with me. That's fair. I will own up to that. But I will stand by my other point concerning optional content. I would even go a step further and state it would be a lot better for everyone involved if Square-Enix would roll out a patch for Shadowbringer for any adventurer just starting the expansion.

Right before the first quest starts there would be a disclaimer that would appear on the screen in big bold letters that would state:
DUDE, IF YOU HAVEN'T DONE THE CRYSTAL TOWER QUEST LINE, THEN JUST DO IT. FOLLOW THAT MIQOTE ALREADY. AND IF YOU HAVE ALREADY FINISHED THE RAIDS, THEN REWATCH ALL OF THE CUT SCENES. YES, ALL OF THEM YOU BIG OAF. THANK ME LATER DUDES AND DUDETTES.
-Yoshi P.

I don't know why I made him talk like he's from Cali but whatever. Anywho, my point is I just got done rewatching all of the Crystal Tower cutscenes, and mostly everything involving the Exarch is NOW starting to line up. Finally. Should have done that ages ago.

[Cleretic]

Right before the first quest starts there would be a disclaimer that would appear on the screen in big bold letters that would state:
DUDE, IF YOU HAVEN'T DONE THE CRYSTAL TOWER QUEST LINE, THEN JUST DO IT. FOLLOW THAT MIQOTE ALREADY. AND IF YOU HAVE ALREADY FINISHED THE RAIDS, THEN REWATCH ALL OF THE CUT SCENES. YES, ALL OF THEM YOU BIG OAF. THANK ME LATER DUDES AND DUDETTES.
-Yoshi P.

The Crystal Tower itself being a big centerpiece of the setting didn't tip you off that this was probably a relevant piece of story?

And for the record, the actual timeline of the required-ness-itude of the Crystal Tower to Shadowbringers:

From 5.0 through 5.2, the Crystal Tower was recommended reading by the developers, but not enforced in the story. There was ample amount of optional dialog if you did the Crystal Tower, but the core plot didn't ask you to and wasn't written as if you need to know what happened (or even saying that it happened at all; if you hadn't done the Crystal Tower then it acted like you just hadn't done that yet).

Come 5.3, they actually make the Crystal Tower required for progressing in the story, as 5.3 onward touches on actual parts of the Crystal Tower story rather than just the existence of the Tower. This is actually done, as I understand it, by multiple requirement gates: a new character is asked to do the raids during 2.x as the raids are current at that time, an existing character is I believe barred from continuing from both 5.0 and 5.3 until they've done it (I know it's at least one of these, probably both).

You're right that a blind spot in this is that they can't account for someone who has done the raids, but has forgotten. But that's just an ongoing problem in basically every kind of storytelling; most of them don't remind you of important details just to make sure you're on the same page when they do the reveals, they just expect you to retain memory, because... well, if you were that flagrant about it then you just blow the reveal for the people who actually are paying attention enough to get it.

And to answer the 'Garlean emperor was an Ascian' question, this is more specifically explained in Endwalker (but isn't necessarily important to Endwalker, it's just clarified there), so I'll section off the answer into two parts. For Shadowbringers: the Emperor was an Ascian at all points where this question would be a useful question to ask, he possessed a Garlean who hadn't done much of note and molded the nation into the Empire we know them as now. Solus Galvus was an Ascian at all points where Solus Galvus was an important figure.

The Endwalker-given specifics:

Emet-Selch specifically possessed Solus at some point during his twenties or thirties, who was a generally nothing-special soldier. Under Solus' name he climbed the ranks of the nation's politics, introduced magitek, and molded the nation from a republic into a totalitarian empire.