In four of the five US services you might be right - but the fifth - the US Coast Guard you have to wait for your rating school. Depending on its popularity the waiting list can be as long as five years (for MST school - Marine Science Technician), unlike the larger services where raiting school comes right after bootcamp.
Either way, you arent going to be 21 by the time you've completed all your training. I was 19 by the time I was a petty officer - and while it never was an issue, technically, at 19, I had the authority of a Federal Marshal within Coast Guard jurisdiction (Act of Congress 1799).
I know the non-rates (E1-E3 Seaman Recruit to Seaman) on the boarding teams were under 21, and not many of the petty officers were much beyond 19, 20. From the perspective of a 38 year old, the J.Os (junior officers) which were with the boarding parties were kids - undergrads with authority.
And these same sort of people, today, are boarding vessels armed - shotguns, M-16s, 9mm pistols. These same sorts of people are right now in Iraq doing security sweeps at port facilities as members of Tactical Law Enforcement Teams, are right now maintaining the security of oil rigs, and assisting naval personell in boardings in the Gulf.
In other words, old enough to kill, but not old enough to drink.