I think this runs into the problem of the writers not understanding or bothering to pay any mind towards logistics. How do beastmen that hate civilization, have no cities or towns, and live in forests, support a large population at all? Sure, they can hunt beasts, but that cannot even come remotely close to sustaining a large population for very long, let alone at all.
If they're dominant in forests, then they should logically be expanding their population to as large as the wildlife of the forest can sustain, but that obviously isn't the case because the Empire's forests are still bountiful with game to hunt and fruit to forage and natural ecosystems to flourish. This suggests that beastmen populations are a lot more limited. Combine that with the industry and logistics required to field all of their warriors with metal weapons, and it feels like beastman armies should be either rare or pretty limited in size. While greenskins get to cheat with population logistics by apparently not needing to eat anything, the beastmen get no such cheats. The skaven...well, even with black goo, the amount of food they'd need to feed their ridiculous population that also has ridiculous population growth...while being almost entirely underground and in tunnels...is immense.
If the beastmen are regularly warring against each other, well, that makes a lot of sense. Not nearly enough food to go around, little social cohesion, rule of the strongest encouraging war as a means of settling differences or competing with each other. Of course, that would make beastman armies attacking the Empire a rare occurrence, but limited bands of beastmen raiding for food and loot a lot more common.