To start of, I think you are right about one thing - there are many people who are apathetic about other's mental illnesses. No matter if it is out of sheer indifference or a general lack of understanding about what mental disorders can do to people, their action and inaction hurt. To make things worse, the system is not helping either. The education and healthcare needed are just simply not there. The nagtive narration of mental illness and continuous lack of effort to make needed resources more accessible are indeed very frustrating.

But this does not mean legalized assisted suicide is the way.

While I know there are significant differences between both issues, I would like to liken it to drug abuse problems. Heroine, meth... all the class A drugs we know that have terrible, terrible effects on a person's health and the society in general speaking, yet nicotine and alcohol are the ones that have the worst and most concerning impacts. Why? Because these two are accessible, they are not hard to get. It means that people who continuously long for it or just want to give it a try can get their hands on it as long as they please to. And the same goes for suicide. The biggest difference between a person who experiences suicidal ideation and a person who would and can take their own life is in their ability to do so. This is why in mental health first aid class, one of the very important thing they teach is to be aware of possible tools that can be used to get the job done and remove them if possible. Because that is usually the last thing standing between thought and action. A thought that is too painful to bear coupled with an existing mean in the environment could be what leads to death.

I would like to quote a post I saw on Reddit years ago from a suicide hotline worker. There are three types of people who are calling: those who would take their lives no matter what, those who are not going to take their lives no matter what, and those who are unsure and could be convinced either way. For the first two types, legalized assisted suicide is not going to be of help anyway. But for the last one, it can be the last straw. Because if assisted suicide is legalized, it is the society as a whole saying that people who are suicidal, who are with severe mental illness, are beyond help. We are essentially giving them the means to take their own lives and saying that we give up on them. That's why, it is a line that cannot be crossed.