Well. It's partly a mental health problem, sure. But it's not just that.
We've got a number of things going on that a lot of other countries don't have.
First, guns are a civil right in the US. Multiple SCOTUS rulings in the last 20 years have affirmed that it's an individual civil right, and not a collective one. (Which would be weird, since everything else in the Bill of Rights is about people, rather than the gov't; the power to raise a military was already listed as a power of the gov't in the constitution, so why would the signatories need to also specify that the gov't had the right to arm the army that it had raised?)
Second, the US is one of the few developed countries that has extremely poor social safety networks. We have a low individual and corporate tax rate (again, as far as developed countries go), so we can't pay for the kind of social services that other countries take for granted. We have comparatively high rates of poverty and a far larger economic inequality gap than most other developed countries.
Third, we have a declining public education system; we've been cutting public education, and putting more money towards selective schools, like charter and magnet schools (and, in some places, public funding for religious schooling), which decreases the quality of education. This shitty education system means that comparatively fewer people--and disproportionately black and Latino people--don't have access to goo education, which limits their career prospects.
Fourth, we have a terrible, broken criminal justice system. We focus on punishment rather than rehabilitation, and people that go to prison often find that their opportunities are sharply limited when they get out, likely trapping them in a continued cycle of poverty.
The latter three things contribute to fairly high rates of violent crimes. The first factor makes crime much more lethal.
The truth is that the rate violent crime in the US is on par with violent crime in the UK or Australia (violent crime referring to forcible rape, assault/battery, robbery, and murder), with Australia having a quite high reported rate of forcible rape, the UK having a quite high rate of battery, and the US dwarfing their murder rates.
In regards to spree-killers, there's not a single profile. The US Secret Service has looked at some thigns that are risk factors, but spree killers are so comparatively rare, and have such widely varied motives, that there's nothing that they can draw definite conclusions on. When I say that these events are rare, what I mean is that commonly reported figures that claim daily mass shootings aren't looking at spree killers, but are looking at ordinary crime--robberies, assaults--involving multiple injuries, rather than an active shooter that's trying to kill as many people as possible. A running gunfight between gang member that sees 2 people killed and ten people shot isn't what most people think of when they thing "mass shooting"; they're thinking of something like the Mandelay Bay massacre in 2017, Pulse Nightclub, or Newtown, CT. Some of the people that are spree killers do have a real mental illness; the Aurora, CO murderer is schizophrenic. Many do not.
There's not a quick, easy answer, because this wasn't something that happened overnight. The idea that we've never had mass murderers prior to Columbine HS is just factually wrong, and Columbine has been 30 years ago now.
In 2021, 8 out of 10 murders in the US were committed with a firearm.
130 people die every day to a gun in the US every day in the same data set.
In 2021, the states with the highest total rates of gun-related deaths – counting murders, suicides and all other categories tracked by the CDC – included Mississippi (33.9 per 100,000 people), Louisiana (29.1), New Mexico (27.8), Alabama (26.4) and Wyoming (26.1). The states with the lowest total rates included Massachusetts (3.4), Hawaii (4.8), New Jersey (5.2), New York (5.4) and Rhode Island (5.6).
The top states are all red. The bottom states are all blue. Speaks to safety nets and education and welfare of citizens correlations as you stated.
The FBI found an increase in active shooter incidents between 2000 and 2021.
Had me at what caused the problem, yeah. However, mass shooters have a deeply significant profile. These are young white dudes with conservative to far right beliefs. This is a demographic whose specific problems are rarely being talked about.
Younger and whiter in general, yes. Conservative, eh, I'm not sure that there's solid data on that. Certainly some of the mass murders have had "conservative" motivations (trying to start a race war, targeting/murdering LGBTQ+ people, inceldom/extreme misogyny, etc.), but that's def. not all of them, and I'm not sure that it's even half. Nicholas Cruz, for instance, or the Aurora, CO murderer. Columbine. Newtown, CT. Shit, Mandelay Bay in 2017; I don't think that those had any traditional conservative motives, aside from, "I want to hurt/kill people because I'm feeling hurt".
Part of the problem you've got with looking at their findings though is that all of the things that they're highlighting as risk factors are really, really common. (Which is fucking horrific, but there it is.) If you made a database of all the people that fit the potential mass-murderer profile, you'd probably have well over a million, possibly 10M people in it. So then you have to find a way of finding out which one of those, say, 1M people will become a mass murderer. TBH, I fit their profile, but I have zero interest in murdering people. (OTOH, I do enjoy competitive shooting, even though I kinda suck at it.)
We're largely unable, or unwilling, to address these deep social issues. And that's shitty.