Your post contains the answers to why gun control isn't the solution.
Guns are the tool used in some mass slaughters yes... but not the only one, and not the worst. The worst was done with airplanes and boxcutters. The second and third worst were done with home made bombs.
I own guns termed "assault weapons". They are no threat to you, because I am not mentally ill nor endowed with such undying hate that I have any interest in going on a "rampage". The only way I will shoot anyone is if they are a threat to me or mine and give me no other viable option.
Possibly 310 million guns in circulation in the USA... almost one per person. 309,999,999 were not used in a massacre this week.
This indicates that mere gun ownership is not the root of the problem.
You said it yourself: mental health issues. Someone who shoots up a lot of strangers is by definition not operating in a "normal" state of mind, typically.
You mentioned poverty. It's true poverty tends to increase crime, but is typically not related to mass shooting incidents or other acts of mass murder.
I'll add one: radical Islam. It's been the motivator for many of the worst massacres of the past 16 years.
There is no gun control solution to mass murder, especially not in a nation where there are already 310 million guns in circulation. Even if there were, mass murders have been committed with homemade bombs, swords, machetes, knives and hammers. The blades tend to be a bit less lethal, but the bombs more lethal, so your net gain is probably zero.
Studies have emerged that Europe has a lot more mass shootings/mass murders than we're generally aware of, despite very strict gun control in most countries.
Even if you banned all private ownership of guns, there's always the black market... where the Charlie Hebdo shooters got their automatic rifles (illegal in France) and rocket propelled grenade launcher (VERY illegal in France!). And there's still bombs... planes... cars and trucks... lots of options.
We'd be better off addressing our utterly dysfunctional mental health system, and maybe taking a second look at letting so many of the Jihad-radicalization-susceptible into the country...