And isn't the legal age to vote also based on the same thing?
Not at all. I, f'rinstance had to register for the draft at 18 (1966) but couldn't vote until I was 21. I had to dodge the draft the hard way -- I enlisted!
Back then, one of the big arguments for lowering the voting age was that if you were old enough to die for your country, you should be old enough to vote. I don't necessarily agree with that logic. Like they say, the only difference between the Army and the Boy Scouts is that the Boy Scouts have adult leaders!
Violence is an ugly thing, but not the ugliest of things. The decayed and degraded state of moral and valorous feeling which believes that nothing is worth violence is much worse. Those who have nothing for which they are willing to fight; nothing they care about more than their own personal safety; are miserable creatures who have no chance of being free, unless made and kept so by the exertions of those better than themselves. Gary L. Griffiths, Chief Instructor, Advanced Force Tactics, Inc. (Paraphrasing John Stuart Mill)