My question back to you, is there a reason why Summer wouldn't/couldn't have had the main job in another era?
Answering a question with a question...how very Fae of you!
The main thing that makes me say it is that it hasn't been mentioned whatsoever. It would be odd of Mother Summer to reveal the whole big secret of the Outer Gates and Winter's purpose, and not tell Harry it once was Summer's purpose. Also, she literally says it was never Summer's purpose and she cannot lie. Unless you're saying Nemesis got to her.
“Holy crap,” I muttered. “Does Summer have a place like this, too, then?”
Mother Summer shook her head. “That was never its task. Your Council’s estimate was fairly close, counting only those troops protecting the hearts of Winter and Summer. Mab has more than that. She needs them—for this.”
I felt like I’d been hit repeatedly in the head with a rubber hammer. “So . . . Mab’s troops outnumber yours by a jillion.”
“Indeed.”
“So she could run you over at any time.”
“She could,” Mother Summer said, “if she were willing to forfeit reality.”
I scanned the length of the wall nervously. It looked like it went on forever—and there was fighting all along its length.
“You’re telling me that this is why Mab has her power? To . . . to protect the borders?”
“To protect all of you from the Outsiders, mortal.”
“Then why does Titania have hers?” I asked.
“To protect all of you from Mab.”
I've emphasised the relevant bits.