That seems more like a pragmatic obstacle than a principled one.
Assuming that wasn't an issue (maybe some 16 year old was able to graduate early) is there any moral reason you wouldn't want him to enlist?
What morality or principle concerns you? Young kids get killed in sports and accidents all the time.
BTW, although seventeen year olds can join a service with their parents permission, Congress wrote a law in WWII, IIRC, that they can’t be deployed overseas until they are eighteen.