The “on the water” laws change from state to state… and from municipality. In PA… it is perfectly legal to stand in a boat while under way, although it is highly suggested to sit. If you are under 12… you must sit, and wear a life jacket on a boat under 16 feet. If they made it illegal to move around on a boat while under way… how would any of the deck boats be used, or large pleasure craft??
Anyway… you will have to check with your state because there may be a law on standing in a boat under a given length/HP.