Guns have been more accessible and readily available for the entire history of the United States. School shootings are a relatively new development.
Access to and availability of guns has been more greatly restricted over that time. With virtually no impact.
Perhaps the desperation and miserable mental health of our population are bigger factors?
Every country you would point to likely has better access to healthcare, education, and much better social safety net than the US. As well as law enforcement and prison systems less focused on restitution/justice and more focused on education and rehabilitation. Other countries also see less recidivism and lower violent crime rates in general.
All available evidence indicates we should be spending much less time and energy focusing on guns and far more focusing on the failures and motivations of our government.