There are so many levels at which this fic doesn't work that I don't know where to start. Maybe I'll focus on biology, as this is my area of expertise.

two hundred for semen extraction and magical stasis

Semen extraction from a kid who just had his first emission? Good luck with that. Hormones start working before sperm production really starts so for a while (each sperm cell takes about three months to produce, while the production of fluids go much faster), kids may, to put it bluntly, fire blanks. They seem to get castrated as quickly as possible, which means many ponies are in for a nasty surprise when they want to become parents.

Not to mention that, as far as horses are concerned, there's that thing called "proud cut", when a gelding behaves as if his balls were still in place. I wonder if they had trouble with that (or maybe, as in any dystopian story worth its salt, such cases were swept under the rug to maintain the positive "castration is the solution to all the world's problems" image). The "history" part was conveniently omitted, so we don't know if Equestria really had some problems with, as Pipsqueak put it, "bad things" in the past, or is it all feminist propaganda? Although at some point Cheerilee says, to quote:

"Most stallions were well-behaved and productive members of society."

Implying she remembers the times before mandatory castration (or at least she read about that somewhere, meaning it's either allowed to say not all stallions were bad, or she's guilty of thoughtcrime). Though then, in the next chapter we have a mention of an old, castrated doctor (though then, we don't know what Rumble considers "old"). Also, "most stallions were well-behaved" – either Diarchy overreacted and castrated the majority for the deeds of the minority, or 'Lee is really on her way to Room 101.

Cheerilee nodded. "Yes, but the violence in yak culture is largely positive violence, similar to violence in athletics," she said. "It's also common to both male and female yaks. We don't know for certain that yaks have the same problem with abuse and rape that ponies faced before gelding became commonplace."

Oh, so it's fine when girls do that, huh? It's just 5k words, yet this verse already feels repulsive.

F all these ponies, female murderers and rapists exist, what is the diarchy doing to stop THEM?

This an interesting take on this idea. It's so common place here in our world that I never even thought about it being an occurrence in Equestria. It's apparently state mandated, too.
This is a thought provoking story, Trick. I'm interested in seeing where you go with it!

What. The actual. Fuck?!

GGAAAAAHHG!!! Those... those... those SINNERS!!