There were very few even before they were restricted. So very little difference. What few there were were the result of Prohibition, another failed solution based on banning something.
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Machine guns were banned because cops didn't have the weapons to counter them at that time. Pretty silly to go up against a Thompson with a snub nose S&W .38.
Yes, prohibition had a great deal to do with banning machine guns, the mobs and outlaws were the ones who had and used them.