1. His Universe is actually broken, dimensional cracks are literally across the universe. Xuanzang says there is no time and
asked him on what he wants to do and it is on priority, why do you think he had to leave everyone to take care of the situation, if he does not stop now it'll cause serious damage, he's the only on that can do it and govern the balance. Even leaving his own family and friends, broke this announcement to everybody, and then they're reeking havoc on Earth, the God Fragments (as seen with Mira, Daewi, Uma, and everyone else). Along with the sixth letter as they're duplicating. 2. Also its not an extrapolation, it is said he can govern all of the universes and all of creation as stated & translated, yes those 2-3 mentions is literally describing
his own universe, she says this, specifically, and as well as that. "Creating balance in
the universe aka his own, even said "or will you loose your power and return to the world". From
their (Mori 'sand Mujin's) battle it caused dimensional cracks in his own, and again she says "... who restores balance to the universe." It's mandatory priority on his end to restore balance in the universe which is
his. A, and B, its his own universe Xuanzang is describing right now because its highly in danger. And C, he's capable to govern the
Universes as per
@karma 's translations. So he has access to the others, just his is in most danger.