Let me try to connect your comment to mine. When this hypothetical person says "go live in a cave", even if your reply to them is literally the words "not that", the meaning is more than simple negation. You're going to DO something. You have reasons for doing it. So in our rhetoric we need to move away from negation. Maybe you'll continue to live in your imperfect house. Maybe you will leave your imperfect house and move into something that is neither that house nor a cave, that's what you will DO. Negating the suggestion of living in a cave doesn't say what you WILL do. But we know you will do SOMETHING.
Like when someone says "we will ban abortion" they do not usually identify the kinds of medical care that will be substituted for situations where abortion would normally be the treatment. Banning and negating can't lead to the thing we actually do. Even if we all agree nobody will live in caves, that doesn't mean everybody lives in houses instead of cars. They're going to live somewhere, and saying "not in caves" isn't useful.
@paco sure. But in most cases there is already a status quo, which is what people tend to mean when they say "not that". As in the situation is not great, someone proposes something and the reply is no that seems bad, I'd rather keep what we have even if I think it is still not great.
Ofcourse it would be even better if they did offer a valuable suggestion, but we can't all have ideas for everything and sometimes it is valid to just say no I do not want that