The relevant question for me would be how many people would be combat ineffective for how long with and without the flu vaccine. Your Claude conversation says things like this:
"The best recent direct measurement is the FLUTES study (JAMA Network Open, 2024), which tracked secondary infections after flu entered US households across 2017–2020. The result: the estimated effectiveness of influenza vaccines for preventing secondary infections among household contacts was 21.0% (95% CI, 1.4% to 36.7%). Note how wide that confidence interval is — the lower bound is nearly zero."
And
"This is consistent with older household work. A 2013 study found no evidence that vaccination prevented household transmission once influenza was introduced; adults were at particular risk despite vaccination — strikingly, 9 of 11 adults with household-acquired influenza were vaccinated in that sample."
So most people on base who were going to get infected and transmit are still going to do so. Some portion of them have a better time with the illness if it does come around, which won't happen all the time. Contrast that with the costs of the program (side effects, time, whatever cons you can think of), and it seems like you might not be in slam dunk territory.