I'm aware when that amendment was drafted and ratified and I'm also aware of what precipitated its origins. And the argument was not just that if you can be drafted you should be able to vote, it was that people who were of draft-age should be able to vote for the civilian government that determines when and how military force is used. So that extends into peacetime circumstances, not just when the country is at war. Also, the idea of lowering the voting age to 18 had been proposed by both Dwight Eisenhower and LBJ, and some states did in fact lower their minimum voting age, however there was no across-the-board federal law doing so yet.
But that final statement in the amendment is the kicker here; you can't deny someone the right to vote based on age, and it goes either way. You can't tell a 19 year old they're too young, and you can't tell a 60 year old they're too old.