How about "different", rather than "more"?
Of course the shooters are
ultimately responsible, unless declared not guilty by reason of insanity.
You keep blaming mental illness, but the US isn't an outlier in this area. Developed countries with similar, or higher, rates of mental illness than the US: France, Spain, Portugal, Ireland, Australia and New Zealand*. Yet, they all have much lower gun crime rates than the US. What's the key difference? It's the quantity and easy availability of firearms in circulation. The math doesn't lie.
Mental Health - Our World in Data
Canada has lower mental illness rates than any of those six countries, yet has higher gun crime rates than they do. We also have more firearms in circulation than those countries, as well.
In the end, it's up to Americans to figure out how - or if - to solve the problem. While it may look like I'm the busy-body Canuck lecturing Americans, it's not from a position of moral superiority. It's the fact that so many crime guns in Canada are smuggled in from the US. So, we have a vested interest. I would wager that any of those European countries I listed above would see increased gun crime if they also shared a border with the US.
Since you mentioned cars, how about compulsory training, licensing, registration and liability insurance for firearms? Across the board. Every state. No exceptions.