I think it's silly to attempt to view the actions of the Garlean Empire with a real life perspective. Even in the World Wars, you're not talking about an existential conflict where the other side is trying to wipe you off the face of the planet. Eorzea is constantly in such a battle against many of the Beastman tribes, and no doubt the Garlean Empire is also aware of the threat the Beastman tribes present. If you're fighting a foe that is clearly comparable to you in overall strength, arguably more advanced in some ways (Cobalt, the highest grade of metal, comes from the Kobolds as per the crafting quest), and have a divine power that seems to be far easier to invoke then your own Gods (Primals sure seem to show up far more often than the Twelve), you ought to be worried about your survival and not take any chances.
It's actually far more bizarre that anybody would attempt to make peace with the Beastman tribes, and even more bizarre that various Eorzean factions haven't been completely wiped out by a primal yet. And since the Primals gets more followers via tempering, there's nothing wrong with the 'purge the weak' attitude the Empire have, because if you don't purge them, you'd be fighting against them when they get tempered by a Primal. When you consider a Primal's strength is directly tied to how many followers it have, it's basically asking for genocide. Remember, the Beastman tribes are very strong themselves, so it's not like you have the luxury of playing safe because due to tempering, any small change in balance can quickly result in a complete steamroll for the Primals. In fact even the Warrior of Light does this when he finally realizes that he's not beating Garuda without killing the followers first, and you'd think that'd be elementary tactic against the Beastman tribes, except it is not.
If you're the Garlean Empire, you probably view Eorzeans as a bunch of idiots that's about one disaster away from becoming the thralls of a Primal. Gaius shows considerable restrain to even negotiate with a bunch of morons that are likely to become servants of a Primal as opposed to actually do anything useful against Primals.