Most often after a mass shooting there are cries for gun control, but almost always what is proposed wouldn't have altered the shooter in question from obtaining a gun.
Maybe he would have got it, yes, but he may have given it back. Australia just finished another
gun amnesty where more than 26,000 guns were handed in
no questions asked for sale with private (legal) buyers/dealers. According to Victoria Police, "In addition to seeing thousands of firearms surrendered and registered to existing licence holders, the amnesty has unearthed some rare and well-kept firearms which have been donated to local museums, the Victorian RSL and the Australian War Memorial." In Western Australia
1242 guns were surrendered, including 186 shotguns, 860 rifles, 196 handguns and 65,618 rounds of ammunition, and also an assortment of high-powered weapons and guns that had been modified.
Previously, Australia's gun buy back scheme (where the government compensated people who surrendered their guns, again no questions asked) was also successful in getting guns off the streets and out of homes where they may not be safely stored. The gun used in the Lindt Café siege was unregistered, and resulted in calls for another amnesty or buy back. There were military grade weapons handed in as well as shot guns. There are ways to reduce the number of guns, legal and illegal, in the US, but again, I don't believe they'll even be done, especially nationally. Without border checks, state laws are useless because people will just cross borders and buy where they can (or get their guns illegally).
There are many ways to implement gun control without banning all guns. Providing incentives like amnesty or buy backs results in less guns on the street. IMO this can only be a positive thing, even if it prevents just one accidental death or one suicide, but I don't see it ever happening in the US.