Protectors of the Plot Continuum/WMG

Chrysanthemum Brown was from a Mary Sue Factory.
That was why she could control Jay and Acacia.

The entire PPC exists to entertain the Flowers.
It only makes sense when you factor in the bizarre qualities of HQ and the insanity of everyone working there. It's all just some kind of (sick) entertainment for them, seeing the others trying to do an impossible task that has infinitely more effective ways of dealing with it and watching people break down spectacularly.

Alternatively, the PPC exists to keep certain people out of the way.
There's no possible way several of the agents could survive in a normal continuum without being arrested. The PPC exists to keep them gainfully employed and out of the way of sane people.

Lux is smarter than she looks.
She's survived too long to really be as ditzy as she tends to seem.
 * Alternately, she's exactly as crazy as she looks, and the reason she hasn't gone into angsty, suicidal craziness is because she's already stuck in gleeful insanity. This, of course, is why the Flowers put her where she is in the first place.

A secret relation exists between the agents and mary-sues, which might be why they are hunting them
Could explain why some agents seem to be in the process of transforming into sues themselves. Maybe it's like in Changeling: The Lost...
 * So you're saying the Flowers are basically Kyubey? Damnit.

Ithalond will eventually retire to Mithlond and sail to Valinor.
It's pretty much his only chance of recovery at this point.

The Flowers serve the stories of Discworld.
The stories don't care what happens as long as they are told, and any significant change (Canon Derailment, Self-Insert Fic, etc.) hurts them. Therefore, they employ the agents to rid them of these parasitic entities.

Even if the Intelligence Agent for My Little Pony Friendship Is Magic wasn't a Time Lord before, s/he is now.
While this Agent was investigating Cupcakes, Possessed!Pinkamena noticed, and saw that s/he knew too much. And we know dying Agents have turned Time Lord to cheat death before.