This variable is largely irrelevant due to the fact that criminals would still have access to such weaponry beyond the law. Just a brief look at Europe shows large black markets for firearms due to the illegal demand there is for a firearm.
I believe a more relevant variable is the fact that most shootings that have prompted elected officials to support gun regulation, have all occurred in private areas where guns aren't allowed to be carried. Had an armed, law-abiding citizen been at a single one of those shootings, there is a large possibility that such shootings wouldn't have occurred in the first place.
To be fair, according to my source about half of mass shootings were committed by people who were legally able to acquire a gun, while a quarter were prohibited possessors and the other quarter is unknown.
Also only a quarter of mass shootings actually take place at gun-free zones.
[Source]
Though to be perfectly honest I have read of many cases of people intervening and stopping crimes using firearms, yet popular media either doesn't acknowledge these cases at all or tries to discredit them. They'll often argue that people who try to intervene will only make the problem worse, which itself is highly presumptive and speculative with scant evidence behind it. This Mother Jones article cites two cases where this happens, while it discredits several legitimate instances of people stopping mass shooters with reasoning such as the civilian was an off-duty cop or Marine without arguing while ignoring that many gun owners are cops or military to begin with, the mass shooter supposedly was done shooting even though that's unfalsifiable and irrelevant because the shooters would have escaped if not for the civilians,
the list goes on and on. I cannot find a single actual study examining the issue, just very biased articles from both sides of the debate that list several examples of this phenomenon happening and using them to bolster their side.
I don't think this is about firearms because the arguments against people intervening apply regardless of whether one is armed or not. It's not about guns. It's about this vile, cowardly idea that only official authority figures are allowed to save other people, whatever the cost, and an implicit belief that intervening in an emergency situation isn't about genuine concern for other people but about prestige and the assertion of dominance, because intervention is a sign of dominance, and we all know we can't let regular people have any kind of power, agency or control in our society.
If you, the reader, don't believe me, poll pro-gun and anti-gun people and ask them about their attitudes toward intervening in an emergency. I would bet you dollars to donuts that the pro-gun people would be gung-ho about handling the situation, right there, themselves, while the anti-gun people will argue that regular people are too stupid or ignorant to help and should wait for a dominant member of the tribe to help regardless of the fact that the victim could die without any kind of immediate assistance. They will even do this when people intervene in mass shootings and stop them while unarmed (by tackling the assailant or whatever). Have you ever seen a nightly newscast about some brave individual stopping a crime that has a cop or another authority figure telling you, the audience to never do the same thing or you'll get hurt? That's a manifestation of this disgusting attitude that I personally find abhorrent.
And it'll never occur to anyone that teaching everyone at least the basics of what to do in those situations in high school, including firearms training where students who pass get their gun license much the same way as teens in middle school get their boating licenses, would appease the anti-gun people while promoting the (what I believe is the morally correct) worldview of the pro-gun people, but who cares about nuance?