Your last couple paragraphs here are spot-on. Hasty laws are rarely well thought out, and this goes doubly when it’s a blatant attempt to deflect from another issue.
I think it’s also worth pointing out even the calls for better mental health are missing the point (though in this case, it’s an understandable mistake). Statistically, people with mental health problems are far more likely to be victims of violence than perpetrators of it (and they’re at particular risk of being their own victims). I get where this line of thought is coming from, as it seems impossible that a “normal” person could commit such an atrocity. But when you look at cases like the Stanford Prison Experiment, you see just how much evil “normal” people can do in the right circumstances. We just need to do a better job at making sure fewer people live through the circumstances that lead to them going evil, and consider enacting gun control measures that will limit the damage they do if this fails.