We should separate the draft age from the enlistment age. The arguments you've put forward are more applicable to the enlistment age: "Is it not immoral to allow people who are apt to make impulse decisions to sign their lives away to the government?" In contrast, with the draft, the relevant factor is the age at which people can make good soldiers, not when they make good decisions for themselves. 18-year-olds can make perfectly good soldiers. In the military, you're trained to follow commands, so making good decisions for yourself isn't very important as many decisions, within the military, are made for you.
Against your argument about the enlistment age, your analogy to alcohol use is a little off because the reasons are different. The reasons that drinking is worse for someone who is 18 are twofold:
The influence of alcohol impairs decision-making which when coupled with impetuousness creates a recipe for social problems. Present decision-making gets impaired through the substance.
If the brain is still developing, it's not a good idea to drink something that we know adversely affects brain development. Future decision-making gets impaired if you've damaged your brain, relative to having not have drank.
Thus, the harms to drinking at young ages are harmful because of the interaction between the age and the substance. So, the interaction of the two factors is more likely to produce harms, which means that we have a stronger reason to curtail young people from drinking because of its negative effect on present and future decision-making, which other types of decisions.
We generally do think that, although the brain isn't at its fullest level of maturity, 18-year-olds are capable of making decisions. This is why the age of consent is at 18 (or in some places younger). The decision to have sex or not is more likely to be a spur-of-the-moment type of decision, but is also can be heavily consequential, from pregnancy, rape, disease and so on. The decision to enlist is much less likely to be on-the-fly; it is much, much more rare for a person to impulsively join the military for obvious reasons. People reflect about major life decisions, using their rational capacities at least to some degree. The same cannot be said about sex as readily. If we were to say to 18-year-olds that we're going to nanny their decisions to join the military, why are we not nannying their decisions in regards to sex, an act much more likely to not be reflective? Or any other major decision?