Many people already load and reload their own bullets in the US because it is significantly cheaper. Good brass can be used many times over and loading equipment consists of an arbor press and some dies. Regulation would make getting it harder and more expensive, but all you would be doing is creating an ammunition black market that funds criminal enterprise with a supply still too large to do much in hampering gun crime.

Responsible gun owners and hunter who practice regularly would be harmed the most because they use tons of ammo. Criminals won't because they might only shoot a few bullets in their life and usually from close range.