Just like you can walk into a store and buy a pellet gun, or sling shot (speaking on a street corner) but not a 45 1911 (like using a ham radio). However dead people, illegals and everyone else can and have voted. You can not have mental problems and buy a firearm, but you can vote and you can get a license to operate a ham radio.
There are far more restrictions on buying a firearm and I am not saying that a background check and ID are to much to ask to do it. EVEN THOUGH THE 2ND SAYS SHALL NOT BE INFRINGED. However the same should be applied to voting as well then if that is what they want to buy a firearm. If there are not illegal votes, what is the problem? None, just like law abiding firearm owners (or 99% of them) do not have a problem with a background check and ID, neither should hardly anyone have a problem proving you are a citizen meeting all the required criteria to legally vote. Do you know what the federal fine is for operating a ham radio without a license (speaking to large numbers of people or broadcasting)? In 2013 a guy in Florida was fined $25,000.