My understanding is that the restriction comes from the great depression, when the government was worried about people poaching deer and decimating the population by hunting more than was allowed

And then we just never got rid of the exception.

Similar to how short rifles were restricted to create additional charges for bootleggers transporting alcohol during the prohibition, since being in a vehicle really benefits from having a shorter gun so bootleggers would cut length off their barrels so they could more easily handle their guns in the vehicle