I'm talking about shelter, food, water, and a basis for living comfortably. We have the resources to do this, today. We just don't have the distribution infrastructure. Money should be something you spend purely on things you want, not things you need.
Given that we built a distribution infrastructure of some kind to automatically and evenly distribute the total food resources of the country, we would see a dramatic change in how money is looked upon and how we use it. No longer will we require money, instead, money is something you earn and use for things you wish to do. We can focus all of our time and energy on furthering our technology, our minds, and the human race in general.
We shouldn't need to buy food. That's the point.
I think that you overstate the scope of things for which a basic services model is better; really, I think all of the things on your list are things where BI works better than basic services.
As far as mental illness goes, that is an interesting problem I don't think GBI would solve. Sure you can give a schizophrenic person a check, but are they going to cash it? Or would you still have some sort of public facility for mentally disabled people? I would hope so.