It does, but it also hoses dedicated reanimation decks. Which we're not - we're a resource denial deck that just happens to have Reanimate in the command zone.

Maybe it should be Yixlid Jailer...

But Priest doesn't even hit one of the scariest reanimator builds: Karador.

I could see it being Hushwing Gryff. It hoses some of the same strategies (Brago blink, Kaalia, etc) while additionally hurting Sharuum, Karador Boonweaver, and several other strategies that Containment Priest can't touch. I think that's what I ended up replacing Priest with in my Alesha mana denial build.