Plenty of mentally stable people only do the one.
If your only definition of "mentally stable" is "they don't murder again", then I guess you could make that argument, but it is ok to just acknowledge the fact that murder is not a healthy behavior. Like you don't have to fight fact on that one. It's just a known truth about the human condition. You can want Luigi out while acknowledging that murder is unhealthy and wrong.
His mental health declined until he murdered someone. It’s not that he is “batshit”- he had a very serious issue that he could not manage on his own. When you isolate from others, can’t work, and only focus on your own pain and violently hurting others until you do it- you are not a healthy person who can mange your own affairs. To me, it’s no different from saying someone “deliberately” slammed their head into the wall, so they don’t “need” a room with cushioned walls.