The situation in Georgia is certainly problematic, and I agree with you that people with certain diagnosed mental illnesses should not own firearms. However, firearms are certainly far from unregulated compared to driving.
Have you tried to purchase a firearm? It's not like going to the hardware store and walking out with a brand new chainsaw. You have to fill out all of the paperwork for a background check, wait for it to come back clean (often takes hours), fill out a transfer/registration form, pay applicable taxes, and then there's a holding period. The only way around the holding part is if you possess a concealed carry or firearm license, which requires training, more background checks, more taxes and forms, and a very long waiting period (usually months) for the permit to be issued.
These same requirements are also in place at gun shows, by the way. You often have to send your purchase to a local FTL for the holdover period, if you don't already have a license.
Also, in regards to the mass murder issue, France was having issues with people driving trucks into crowds a few years ago. England has mass stabbings, and Australia has machete sprees. The truly alarming thing with the US is the growing frequency.