It could be reasonable but like I said, it's a massive stretch. Flu vaccines are not designed to stop Alzheimer's. There is no argued or known biological pathway through which that might happen. Alzheimer's experts have not previously identified flu vaccines as doing anything that might help. And it probably isn't flu itself causing Alzheimer's because, as I've noted elsewhere in this thread, flu vaccines don't appear to have actually reduced overall flu mortality and some studies show negative effectiveness.
I don't think there's a really killer argument here in the abstract: I personally find it unreasonable to imply causation from any medical intervention to any possible outcome based on just a correlation. Yes, it's more reasonable than Nick Cage being associated, but not reasonable enough. That's a judgement call however. I am guided in it by the massive costs and problems created when scientists claim vaccines are miracle cures without sufficiently robust data.
https://www.healio.com/news/primary-care/20200302/flu-vaccin...
I don't think there's a really killer argument here in the abstract: I personally find it unreasonable to imply causation from any medical intervention to any possible outcome based on just a correlation. Yes, it's more reasonable than Nick Cage being associated, but not reasonable enough. That's a judgement call however. I am guided in it by the massive costs and problems created when scientists claim vaccines are miracle cures without sufficiently robust data.