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Yeah, the whole "Winter gets to fight off Outsiders, while Summer is in charge of fighting off Winter" thing is stupid. It seems like it exists to make Winter (Harry's side) the more important one.

Personally, I think it could have worked well to have Summer and Winter be taking turns. It's already established that Summer and Winter take turns being dominant, switching at either the Equinox or the Solstice. I would have liked it better if they took turns fighting off outsiders/replenishing their forces.
Of course it's always possible that Summer is ALSO fighting off outsiders. Each side is intentionally kept in the dark about the other so as to avoid using it as leverage for any potentially balance-breaking trickery (for example, Winter pulls some troops off the frontlines, pretends they were killed, and has Summer pull troops from the heart of Farie to reinforce them, then uses the "Dead" troops to launch an attack).

That could actually make more sense. In Summer Night, the plan was to use the stone table to hand the power of the Summer Knight over to Winter, creating an imbalance. But if Aurora was infected by the Nemesis, she would be trying to help the outsiders.

Tipping the balance of power in favor of Winter would be bad for the world, but it would only help Winter fight off the Outsiders.

However, if there was another front, one that Winter didn't know about, but Summer did, (just as Summer was unaware of Winter's gates), then tipping the balance in favor of Winter could cripple summer's ability to protect it's gates.
If Aurora dosn't even know that Winter has gates to protect, then from her perspective it's the equivalent of stealing a tank from the army, and giving it to a street gang.