I think that outright prohibiting "mentally ill" people from owning firearms prevents some people from GETTING the help they need in the first place.

I own a gun. Several. But I've also been suicidal in my lifetime. Quite a few times. And for years I didn't want to get the help I knew I needed because I was terrified they'd force me to hand over my guns. (I realize now this was an irrational fear. Moving on.) Still, if my pdoc ever asks me if I own any guns I will most certainly lie. Call me paranoid.

But some people might know very well they need help and they may choose to go without because the fear of big brother is greater than the fear of an unchecked mental illness. At least that was my personal experience.