Mental illness as a culprit is a pretty tired explanation of these events. Statistically, mentally ill people are far more likely to be victims of violence than to perpetrate it, and in many of these events, there is a clear lack of diagnosable or observable illness to begin with. Besides that, even if you don't believe the numbers here, it's possible to improve mental illness treatment and legislate gun control responsibly, it's not an either-or thing. TLDR "Mental illness" is a very tired, very poor explanation for the phenomenon, not even to mention it perpetuates and encourages stigma.
> Statistically, mentally ill people are far more likely to be victims of violence than to perpetrate it
I think this is one of cases where a broad label like "mental illness" obscures more than it clarifies. There are some subgroups of people with mental illness (schizophrenia, bipolar, antisocial personality disorder) who are more likely to commit violence than others, especially when combined with substance abuse. But of course that fact doesn't generalize to all people with mental illness.
https://www.apa.org/monitor/2021/04/ce-mental-illness