What function does it serve other than arbitrary inconvenience?

That's literally it. The original intent was for handguns to be restricted as well. The $200 tax stamp at the time was prohibitively expensive, pricing them well beyond the means of most americans. They didn't count on the federal reserve raping the dollar with interest, so these arbitrary inconveniences is designed to make most people not want to bother. The ultimate goal is total gun restriction, which the second amendment forbids, so they have to whittle away at our rights with thousands of tiny cuts. Any gun control is good in their eyes, no matter how arbitrary and frivolous.