The flu vaccine is a special case as it’s changed every year.
https://en.wikipedia.org/wiki/Smallpox#Prevention
"Smallpox vaccination provides a high level of immunity for three to five years and decreasing immunity thereafter. If a person is vaccinated again later, the immunity lasts even longer. Studies of smallpox cases in Europe in the 1950s and 1960s demonstrated that the fatality rate among persons vaccinated less than 10 years before exposure was 1.3 percent; it was 7 percent among those vaccinated 11 to 20 years prior, and 11 percent among those vaccinated 20 or more years before infection. By contrast, 52 percent of unvaccinated persons died."
“It is recommended that adults get a Tdap shot for one of their tetanus boosters.” https://www.verywellhealth.com/booster-shots-1298291
It simply reduces the number of injections when you get multiple vaccines at the same time.
No, it is not (just) timing.
"Three doses gives better protection than two doses ever did" (1)
Immune response is very complex (2) and we're not experts; but we should not measure it in just 1 number: that gives the impression that the response is a range from "high alert for this recent threat" through to "threat forgotten" - effectiveness did not last that long.
There are there are other states as well when the threat is "on file" in the immune memory. Another exposure months later influences this process. My guess is that the evolved heuristic is that "a threat that recurs more is worth remembering better".
1) https://twitter.com/PaulMainwood/status/1460191035531878405
2) https://www.theatlantic.com/health/archive/2020/08/covid-19-...
3) https://www.theatlantic.com/science/archive/2021/09/waning-i...