Correlation does not imply causation. Various parts of Canada also had prohibition during some of the same timeframe. The drinking age there is also set per province, which interestingly, is also the same for the USA. For example the drinking age in Virginia is 18 for beer and wine but 21 for spirits. When I was growing up in Louisiana, there was a weird loophole law; you could be 18 to buy alcohol but had to be 21 to drink it. It was changed to 21 outright shortly after I turned 18 of course. Although the states can set their own age, the National Minimum Drinking Age Act, which was passed in 1984, forced the States to lose some of their federal highway funding if they set it lower than 21. This effectively set the national drinking age to 21.
I agree with you that at the very least members of the military should be able to purchase liquor. It's asinine that somebody can face bullets, or vote, or get legally married, but not be mature enough to purchase alcohol. Thanks MADD!