Army recruits are still given MMR, DPT (or DTP, whichever adults get), and polio, as well as flu. They may be given chickenpox now too (it wasn’t available when I went through basic). People who are sent overseas into war zones are also given smallpox.
Since there will always be some recruits who weren’t properly vaccinated, some people who lived overseas, or weren’t US citizens, some people whose parents were anti-vax, others were just negligent, missed follow-up boosters, etc., and a few who didn’t respond to a vaccine, but will respond as an now, the policy is just to vaccinate everyone. The alternative is to have everyone who is vaccinated produce records showing their vaccinations, and that can be a paperwork nightmare; there’s no danger in being vaccinated again for something you are already immune to, so so what if you get an extra vaccine? there were about 250 women in my company, and 1,250 people altogether in my battalion training at the same time; not one person got sick from a vaccine. FWIW, you get them all on the same day, too.
Adults are vaccinated during outbreaks sometimes, too. There was a measles case in a dorm on my college campus, and every student was required to show proof of prior vaccination, or get a vaccine. The vaccine was free, and getting my paperwork from New York was a pain, so I just got the shot. Faculty and staff were getting it too, on a voluntary basis. The lines were long, but they moved fast.
If an adult has not had chickenpox, that adult really should get the vaccine, particularly if he becomes a parent. But many people don’t think to bring it up with their doctors, and since there aren’t family doctors much anymore-- that is, the parents and the newborn are seeing the same doctor, it may not occur to the doctor to bring it up either. By brother had the chickenpox as an adult (21 years old), and was so thoroughly miserable. I had them when I was three, and don’t really remember them.