An egregious straw man. I never said the DM has to have mastery over every class, I said (by implication) that he has to have mastery over every class that's involved in his campaign.
I find it hard to keep reading when you open with nitpicking.
If the group he's DMing consists of a fighter, a cleric, and a monk, then the DM has to know how the fighter, cleric, and monk classes work AT LEAST as well as his players do. He doesn't need to know how the bard class works because he's not DMing a bard. Thus, he should spend as much time as is necessary to become thoroughly familiar with the ins-and-outs of the relevant classes, which is certainly more than a mere glance through the PHB. Thus, back to the original point of this thread, the DM who disallowed the used of XGTA in his campaign may very well have decided that the not-insignificant amount of time and energy it would take to become thoroughly acquainted with the class options presented therein that were being proposed for use in his campaign (which, I will insist, is what he SHOULD do as DM) was not time and energy he was willing to spend (a perfectly legitimate decision, as far as I'm concerned).
So, back to the non nitpicking part of the discussion...see my previous response. You keep stating that it's required, but won't extrapolate any reasoning for that conclusion. I find the conclusion entirely without merit, both logically and experientially.
The DM needs a basic understanding of what is on the character sheets. That's it. The general rules are vastly more important, but only in a game with serious imbalance issues would the GM need to have the same degree of knowledge of the specific character options in play than those who are actually using them. 5e isn't that game. 5e doesn't require constant DM oversight of player abilities just to run the game without it falling apart at a basic level, like in some previous editions. The DM can simply focus on running the game world, on reacting to the player characters, and giving them things to react to, and building a story and a world in the process.
For extra credit, let's examine this further, specifically in the context of what I started out saying here. IE, the DM doesn't need to put in any extra effort just because someone is using a subclass from a new book.
There are two possiblities here, and either way the idea falls apart.
a) The DM has mastered every class and subclass in the PHB, which means that the PHB options aren't any extra cognitive load in the context of a new character, but also means that DM has very advanced system mastery of 5e DnD.
2) the DM hasn't mastered every class and subclass in the PHB, in which case any subclass or class not already being used will be just as much cognitive load as a subclass from a new book, because both are new in terms of whether or not the DM has already mastered them.
In a, the DM has a level of system mastery that renders new options like a subclass (which are quite small in 5e) trivial to understand. If he can't look at the Scout Rogue and tell if it's unbalanced with other options available, he couldn't have mastered the entire PHB already.
In 2, the DM would have to also ban options not already in play in order for banning Xanathar's options to be consistent and sensible. ie, "I've only mastered knowledge of the specific options you are already using, so you have to pick from that list for new characters."
If you want to nitpick the difference between "literally no additional cognitive load" and "effectively no (ie absolutely trivial to the point of it being non appreciable) additional cognitive load", find someone else. I don't care about nitpicking arguements.