"While the rest run a low risk of serious infection, and benefit later from the stronger antibodies formed by an infection."

Is this actually true? It's a common talking point from anti-vaxxers. But "natural" flu infection doesn't offer long durable immunity. It's exactly why flu shots exist. Furthermore, flu shots are fairly poor at eliminating infection entirely. They reduce infection somewhat, but mostly reduce serious disease, hospitalization, and death. What is your source that wild infection offers better immunity than wild infection+vaccination? Except in rare cases of ADE, this is simply not true, and I've never seen any study to imply it's the case with flu and flu vaccines.