He did it with a handgun and an AR-15
Talk about assault weapon bans is entirely missing the point. An AR-15 is a semi-automatic weapon chambered in 5.56x45. America has tens of millions of such rifles. A lot of them are AR-15 shaped and class as "assault rifles", but most of them are hunting rifles of various sorts. AR15s looks dead scary and military and shit (first picture), but there are far more "ranch guns" which fire the same ammunition out of essentially the same weapon in essentially the same way (second picture).
Ranch guns are used to go down to the postbox by people who live in bear country, and for hunting small game, and for dealing with wolves in cattle country. If you are a maniac who wants to shoot people in a club, the practical difference is zero: the laws on assault weapons are about the angle of the hand grip and the extent of the forearm and so on, but it's still a thing that goes bang every time you pull the trigger. There are also versions of the Ruger Mini 14 chambered in 7.62x39, which from ten yards away will be exactly the same as an AK47 if you get shot by it. It doesn't matter that the Mini 14 doesn't look as military (even though, actually, it's basically a 1950s military gun) it'll kill you precisely the same.
In a country with at least one gun for each of the 350m people, worrying about the presence of guns is irrelevant: even if you could wave a magic wand and have complete gun bans enacted in every state, you don't know where they are (you don't have to register guns other than exotic stuff which requires a federal firearms license). In the UK, there has been gun registration since 1916 and the numbers always were tiny apart from break-action shotguns. The ban post-Hungerford on semi-automatic rifles was easy to enact, likewise the post-Dunblaine ban on handguns. In the US, there's tens, perhaps hundreds, of millions of both, unregistered. The question is what makes people use them, and how to stop that, because you just won't be able to control the weapons in any useful way. It'd be lovely to think you can. But you can't.