The whole "what about illegal guns" is a fake, confected argument anyway.
Almost all of these mass shootings, including the school shootings, were done with legally obtained weapons. They simply wouldn't have happened if, like Australia, it was virtually impossible to obtain these firearms legally.
Its demand and supply. Black market guns are cheap in the USA because of how readily available guns are. If you remove legal firearms from the average joe, black market firearms will skyrocket. Meaning, your depressed, angry or mentally ill will not even get close to accessing such weapons because organised crime will corner the market.