But the big issue is "why would the DM give an NPC wizard this subclass in the first place"? Subclasses are aimed at PCs.
The answer to that is likely pretty simple: there is a desire to have at least a casual appearance of PC--NPC equivalency. If subclasses represent actual things in the world (crunch and/or fluff), it makes sense for an NPC who participated in the same thing to have the same features.
I'm going to go further. I'm going to claim that the PHB presents at least some classes--and Wizard is one of them--as if it were an actual thing in the world amongst NPCs. The PHB describes a world where there are NPC wizards with various schools of magic. Sure, the statblock they give us for a
mage in the MM doesn't include that, but I interpret that as meaning that the statblock is intended to be a quick and easy simplified statblock suitable for use with "most NPC wizards". Additional statblocks were put out in different books explictly representing mages of specific schools.
Now, you don't have to run in that way. This time around WotC tried to accomodate multiple perspectives. So they present a world where classes and subclasses can be something in the world that NPCs have, but they give us simplified NPC statblocks so you don't have to build them yourself and use all the rules. And then they let us decide what is true in our own world with those toys.
They do not present a
world where classes and subclasses only exist for PCs--they just give us simplified
mechanics so that we can skip using them for NPCs if we so choose.