That is one study in children. And it looks like the most plausible explanation would be that catching actual influenza confers resistance to non-influenza inf

That is one study in children. And it looks like the most plausible explanation would be that catching actual influenza confers resistance to non-influenza infections, which is inhibited by preventing influenza. And if that is due to stimulation of innate and intrinsic immune defenses then that would explain why children show a high signal for that. There's a whole lot which isn't clear about that, it isn't clear that it affects adults the same way. It isn't clear that it is conceptually possible to have an influenza vaccine which doesn't do that. And it isn't clear that is a net negative since influenza tends to be much worse than other respiratory viruses (up until a few years ago anyway).