Are there countries where guns have been banned, and mass shootings increase?
Are there countries where banned guns have been allowed, and mass shootings increased?
You trade one for the other. Mentally unstable/unhealthy people commit mass violent acts regardless of the tools available.
In practically zero cases of mass shootings was the assailant completely mentally healthy. Taking away one particular violent tool is not going to solve the mental health problem in this country.
Which, btw, are all regulated in the US.