Without extremely large amounts of ammunition possessed by the shooters, the death tolls of the recent mass shootings would not have been nearly as high.
Switzerland, for example, REQUIRES gun ownership by citizens, but strictly controls access to ammunition. Gun violence is much lower there.
If moderate limits on the amount of handgun and rilfe ammunition that could be purchased during any month were to be enacted, along with strict background checks before ammunition could be purchased, gun violence could be reduced. Stolen guns would be less of an issue, sales of guns at gun shows would not be an issue.