Comment by the_interloper

Short answer is that guns are in the constitution, but radios are not.

Longer answer would be that there are already systems in place to prevent transfers of firearms to and from parties that should not possess them in the US. Purchasing a gun at a sporting goods store involves filling out paperwork that can take a long time.

Buying a ham radio is as simple as going to a store that sells them and giving your call sign.

You could (depending on where you live) shoot off a gun in your backyard as long as it doesn't disrupt your neighbors. You can't key up a radio in your backyard on an band you don't have a license for without potentially disrupting someone in some other part of the world.