At the very least the reduced access would reduce occurrences and fatality rates. UK and Australia are probably good comparable cultures/case studies.

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?

Other countries have their own version of mass shootings. They often involve knives, explosives, or vehicles instead.

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.

> They often involve knives, explosives, or vehicles instead.

Which, btw, are all regulated in the US.