I used to think that way; especially in that every once-in-a-while, a flu strain comes through that affects older generations less, because it's like something they saw decades ago, but youngr people haven't yet. So, why not get every year's best guess for upcoming flu strains – & even if it misses this year, maybe it'll help years or decades from now?
However: it turns out that some of the usual case for yearly flu shots is little more hand-wavy than I'd realized.
Flu-like illnesses aren't as well-tracked as the stats might make you think - with an awful lot of grouping under "influenza-like illnesses" of non-flu diseases (that aren't helped by flu immunization), or tallying with all pneumonias. I have a strong sense that pre-COVID, normal "flu deaths" stats were already being exagerrated as part of the campaign to remind people to get flu shots.
For example, in late 2018, part of the CDC's push for more vaccinations estimated the previous flu season was the deadliest in memory, with 80k deaths, and that previously, the worst year had been 56k deaths: https://www.statnews.com/2018/09/26/cdc-us-flu-deaths-winter...
But in their current estimates, that same flu season only killed 52k - and not a single season of the last 10 reached 56k: https://www.cdc.gov/flu/about/burden/index.html
(Some have been pointing out such issues for a while, such as in this 2005 BMJ comment, "Are US flu death figures more PR than science?" – https://www.bmj.com/content/331/7529/1412.)
This actually came back to bite public health authorities during COVID when even the harder data on early COVID mortality could be characterized, against inflated flu-severity numbers, as "no more than 10x worse than a recent bad flu season". Truer (smaller) flu numbers likely would've led to instead an "at least 10x and probably 20x" comparison.
At the same time, it's quite hard to track the yearly effectiveness of flu shots against strains that often don't not match those chosen when vax production begins. In normal years, even suspected flu deaths don't necessarily lead to a lab-determined confirmation of any infectious agents involved.
You can see how little researchers trust the consistency of data on flu cases in the very research highlighted here. If you think flu vaxes prevent Alzheimer's, one obvious mechanism to theorize might be: actually getting the flu increases Alzheimer's risk, the shot reduces flu cases. But they don't even run that analysis, because they don't trust the data on actual flu cases suffered in their samples as being unbiased. (They write: "Fourth, we chose not to include influenza infections in our analyses because of concerns surrounding influenza infection misclassification in retrospective studies of administrative data [56]. Similar to the authors of a recent study investigating the flu vaccine’s association with dementia risk in a VA cohort [20], we concluded that the potential bias from frequent misclassification of infection status outweighed the potential benefits of including this factor in the analysis.")
Finally, and this is the kicker which might knock me off my previous habit of annual flu vaxes, until I'm at a more-frail age, is that there was growing recognition before COVID that regular, mismatched flu vaxes might actually increase susceptibility to some future strains.
You can see a bit of discussion of that in this 2019 guide to the "changing science of flu shots" – https://www.statnews.com/2019/10/14/updated-guide-changing-s... – specifically bottom "Can repeated vaccination actually backfire?" section.)
Two mechanisms that might contribute are imprinting (overspecializing immunity to the 1st strains seen, slowing later) and urgency-fading (training the immune system "we see a batch of these paper-tiger threats every year & they never create actual illness, so we can tamp down our responses to this whole class of agents").
This suggests to me that, even as a big fan of vaccination, I may want to use it somewhat more sparingly: when a specific strain has a higher risk, when a specific formula is well-tuned to an emerging threat. Otherwise, both for me & the community, I might be dissipating the benefits before they're urgent.