... okay, it's an artificial barrier in that the mint has set up this schedule for reasons that have nothing to do with why anyone's face is on the money instead of anyone else's, but it's not artificial in that those reasons are actually practical and have to do with making sure our money continues to function as money.

Which, come to think of it, is almost certainly what the real Hamilton would have considered important. Possibly even more important than making sure his face stays on the ten.