Bit of a red herring : the majority of fire-arms used in mass shootings have been legally obtained and held, often not by the shooter but by the family of the shooter.
Bringing up the mental health of said shooters is another red herring : its an obvious stance to take : 'only a crazy would kill ten/twenty/thirty kids!' : but nobody seems to have noticed this craziness enough to intervene beforehand. Its the old 'they seemed such a quite person' routine when the cops are digging up the bodies from under next door's patio. The signs of 'craziness' gets manufactured after the event : 'he always wore odd socks!', 'She wore white shoes before Labour Day!' and the old favourite 'he had funny eyes!'.
Quite how any medical professional can predict future mental health concerns, never mind how you could legislate the powers to act upon them, is a matter far more concerning than any alleged assaults on second amendment rights.
The final nail in the coffin of the alleged difficulty in obtaining a firearm is that the USA has 400 million of them that are, in the main, legally held. 40% of households have not found the task of passing background checks or wait times to be insurmountable.
The states are notorious for the complexity of differences in many laws. The serving and provision of alcohol is far more difficult a legal hurdle in most than owning a firearm is.
My own view is that who can gain access to legally held firearms is more an issue that is in need of resolution than easing the buying of them is.
There are the majority of owners who practice safe ownership. A sturdy gun-cabinet and keeping to the good habits of locking it is one.
Be honest, for a teenager its easier these days to 'borrow' the gun collection than the family car.