I think it's mentally lazy to just lump all mass shooters into the mental illness category. Obviously there is something wrong with them to allow them to commit such atrocities. However, these people account for a small percentage of people dealing with mental illness, even the same illnesses in a lot of cases. There must be some sort of differentiator which causes one person to do what hundreds others don't.
That argument also stops any other discussions dead in the tracks, as if it's possible to actually fix the mental illness issue. But the focus is put so much onto the mental illness issue that any other solutions are seen as bandaids and will ultimately be ineffective.
Tl;dr stop placing the onus on mental health.