Because the DMG wasn't finalized when AL started
I did a bit of digging, and found this article from December 2014: (excerpt, emphasis added)
Rules contained in the Dungeon Masters Guide may be permitted in future storyline seasons by future versions of the Player’s Guide. Until then, the Dungeon Masters Guide can only be used in D&D Adventurers League games to look up magic items and for general advice on how to run games. This rule was necessary in part because the book was still in editing when the D&D Adventurers League started.
This was written by Art Severance, who was Regional Coordinator for the US Far West region at the time that article was written (I'm not sure if he still is).
Variant gameplay rules cause inconsistencies between tables
The same article also states,
Just as the name implies, the D&D Adventurers League is a league game, in which everyone plays by the same rules, whether they always play in the same place or play all over the world. Characters within the League are portable, so a player who visits another area or moves there or who plays in an online game expects to be able to play his or her character there without having to make any modifications and without having to learn any local rules.
Allowing DMs to decide whether or not to use variant rules that modify gameplay, such as flanking, would mean that there would be "local rules," which runs counter to the philosophy that rules and gameplay are identical between AL tables.
Note that in V3.0 of the FAQ, nearly all of the variant rules that are allowed only affect characters, not gameplay. The one exception is playing on a grid, which I'd argue is a well-accepted, almost standard rule.