I think this also makes sense, I know when I was younger I was extremely frustrated to see adults making really bad decisions for my country that will have a much longer impact on my life than it will on theirs.
I think a minimum age makes sense, I don't think someone in elementary has any point in voting since most likely they would just do what their parents told them. But by 16 you are generally making your own decisions, your figuring out your adult plans, and not following everything your parents say.