Incidents like this, though alarming, are vanishingly rare. There have been something like ~170 mass shootings in the United States since 1966 (the UT sniper), resulting in ~1200 dead, according to a Washington Post tally. That is a minuscule number of deaths and perpetrators. 30% of the population does not need to be monitored in a national database because of this small number of people. Nor do everyone's guns need to be taken away because of this tiny number of people.
An alternative solution might be "media control", less reporting and headlining of shooters and shootings, to prevent copycats, sensationalism and the appeal of making a "statement" of this kind by going out and killing a bunch of people. Events like this percolate through the public consciousness and eventually erupt again; shooters are inspired by the stories of other shooters. This story itself might be more deadly than the gun the shooter was carrying, in the long run.
Rather than attempting to restrict the activity of the 99.9999% of people who don't commit mass shootings, perhaps we could build a media culture that isn't built on making money off the selling of lurid stories of violence?