Mmm, I'm not really sure how much I like the idea of the Horned Rat smiting Skaven Necromancers- he doesn't really strike me as the smiting kind of god, and I generally don't like the idea of the gods being able to literally disintegrate any of their followers wherever they may be the instant they do something they don't like, because it should show up a lot more often if that was the case. But influencing the Skaven to hunt down any of their own who dabble in the art? Absolutely.
The way I see it, every Skaven who ever lived would, if given the ability to convert their followers into mindlessly obedient slaves, try to do just that. But every other Skaven also knows that, because they would do the same thing in their position. So the instant a Skaven starts dabbling in Necromancy, every other Skaven regardless of allegiance gangs up on them, because they know that it's only a matter of time until they're next on the chopping block. There is no "wait until you get the opportunity to stab them in the back", because they know that the Necromancer would immediately kill and raise all of their followers out of paranoia, because that's exactly what they would do in their position. Skaven society relies upon leaders needing followers, and followers being convinced that they'll eventually be able to backstab their way to the top. The moment you introduce the ability to create backstab-proof followers, it starts to consume itself in a feeding frenzy as everyone scrambles to either stop the nascent Necromancer from turning them into a mindless undead, or to seize that knowledge for themselves.
So overtime Skaven society would learn to recognize that whenever someone starts studying Necromancy, a civil war invariably erupts that kills them and everyone in their vicinity, and would evolve a cultural bias against doing that. Sure, every so often things would flare up because Skaven are naturally inclined to think they are the one who's cracked the code and figured out the One Weird Trick to be able to harness Necromancy without being killed, but such incidents are ultimately self-extinguishing because not all Skaven can use magic, so eventually the chain of backstabs will lead to the necromantic lore falling in the hands of a Skaven who can't use it, and thus they'll destroy it to stop other Skaven from using it against them.
The notion that Skaven may have better built-in mechanisms to cut off the spiral of civilizational self-extinction compared to humans (climate change, nuclear Armageddon, etc), strikes me as both hilarious and also very sad.