Legal ownership of concealable weapons and automatic firearms is already difficult in a number of states, especially cities with high gun violence.
I'm not sure what you mean by "automatic firearms," but what you describe is limited to a very small number of states, albeit some of our most populous. Counterexamples are legion, 42 states have "shall issue" concealed carry, that's like 72% of the population before the COVID flee big cities demographic changes to the extent they're lasting, and so far this year three states are improving that to "Constitutional Carry," a total of half the states in the union!
For how we got here, "The American Indian foundation of American gun culture" is essential reading: https://www.washingtonpost.com/news/volokh-conspiracy/wp/201...