As a thought experiment :
Lets imagine doubling the number of gun free zones in the US.
I don't think that this would cause an immediate doubling of massacres.
For this reason; even though gun free zones are just as needed for a massacre to happen as the guns are, there are many gun free zones that go unused by murderous maniacs every year, so there must already be plenty of gun free zones for each potential murderer to choose between.
So doubling the number of gun free zones might make no impact on public safety , or a very small difference as murderers might enjoy slightly greater convenience.
Cutting the number of gun free zones in half might for the same reasons have little impact , half as many as we now have would still be many more venues for mayhem than we have madmen ready to use them.
These guys are fewer than one in a million of us , probably by a factor of five or more, not enough to fill a single prison. This suggests that the scarce resource that could be curtailed most profitably is the guy willing to commit such a crime. I wish this were really simple , but the rare individual ready to commit mass murder is not obvious to detection and their small numbers make them hard to find not like a needle in a hay stack , but like a needle in a needle stack.
The simplest feasible means of making a large reduction in mass murder might be the 100% elimination of one of the three requirements. Guns , collections of helpless victims, or miscreants of this peculiar type.
I suggest that for the USA the simplest and cheapest part of this triangle to eliminate would be gun free zones. This might not reduce the number of miscreants nor disarm them , but whatever fraction of them are cowardly would be out of the game .