I disagree with your first point. Anecdotally it seems that these 'crazy' people in Australia do not go to the eoffort o obtain an illegal gun and go on a rampage; whereas it is much easier in the US (or they might already have them).
Yes there are assault weapons here in the hands of criminal gangs, but far pewer on a per capita basis, and generally the gangs tend to keep it between themselves.
It is hard to kill someone with a screwdriver whereas one nervous moment with a gun and someone can be dead
Also they might be able to get a weapon illegally but it would be harder to get as much ammo and as many automatic weapons, especially teenagers who have limited contacts and funds.
The shooter in this last incident would probably had trouble getting weapons and not have been able to cause as much damage even if he did get hold of a gun illegally. It would also make it easier (or at least more chance) for authorities to capture guys like this before they go on a shooting spree if they are buying weapons illegally as they might get word of it before any damage is done.
Tighter gun controls might not completely stop these shootings but it would make it a lot harder for depressed teenagers to go shooting up schools full of kids.