I'll add to the other commentators that we manufacture more than 12
billion rounds a year, and import quite a few more (especially as of late more .22LR, rimfire production is pretty much fixed at 3 billion per year due to manufacturing dangers and realities, including the reluctance of US manufacturers to buy new capital equipment that can only be used for it).
It would also strong discourage responsible gun ownership, by discouraging people from maintaining their skills. There are, what, way over 12 million who have concealed carry licenses in the US (the number is growing very rapidly and 12 or 12.5 is only the latest and a bit old), more and more states dropping license requirements (it's up to around 10, with Missouri likely to be added this month), and semi-automatic handguns are the overwhelmingly preferred design to carry for many good ergonomic, reliablity and effectiveness reasons.
Legally owned full-auto weapons simply aren't a problem, there's 2 known crimes committed with them, and one of those was by a police officer.... With their numbers limited by a 1986 law to around 200,000, and the inherent cost of firing lots of rounds from them, they're already mostly "a hobby for the rich" as c22 points out. Something you can see echoed in the former Democratic governor of Kansas Kathleen Sebelius signing a law making them legal again after many many decades.