It's my understanding that it is already nearly impossible to purchase weapons that can cause outsized damage.
Three factors contribute to "outsized damage": mass of the bullet and load of the cartridge/shell, which mostly determines the total kinetic energy (colloquially called "stopping power") delivered to the target; rate of fire; and distance to target.
Assuming we agree that sport shooting and hunting are legitimate purposes for the use of firearms:
- The "stopping power" on the bullets sold really cannot be reduced. Large game targets such as deer and wild boar require much higher stopping power than are required to stop a human.
- Distance to target: since this is situational there really isn't much that legislation will help.
- Rate of fire: firearms are _made_ as single-action (bolt/lever/switch), semi-auto, and burst-fire/full-auto, with the latter only available to the military (and maybe SWAT units.) Most rifles and shotguns used for hunting are single-action. Pistols are usually semi-auto, which has legitimate sport-/trick-shooting purposes as well as being useful for scaring off smaller predators while out hunting (wolf, wildcat, maybe bear, etc.) If I recall correctly full-auto weapons are already illegal.
That leaves semi-auto rifles. I'm a little skeptical on the utility of semi-auto rifles for hunting, but larger game might require several quick shots with the right stopping power to bring down (again, wild boar fit this.) Maybe there is a little legislation that can happen here to limit the availability of semi-auto AR-15s to target/sport shooters or specific hunters, but it's hard to imagine carving out legislation specifically for that.
But when it comes down to it, there's not really a great way to prevent a quiet, lone-wolf type killer. A shotgun and pistol in close quarters will do as much or greater damage than a pair of AR-15s, and both shotgun and pistol have legitimate uses.
What I personally think is a better solution is to write legislation that adds responsibility to gun ownership. Firearms should be locked in a secure safe when not in use and access to the safe should be closely monitored by the owner of those firearms. Immediate action should be taken by the owner to report any unauthorized access, or access by an authorized person who is suspected to be suffering some mental health issues, to the police. Failure to secure firearms or to report unauthorized access in a timely fashion when said firearms are used to commit a crime should result in the firearm owner being at least partly culpable for those crimes.
Owner culpability won't solve all mass shootings, but it should start to eliminate some of the culture of callous disregard for human safety that some families seem to exhibit when it comes to handling firearms.