Yes, that's the fundamentalist libertarian perspective. Like most fundamentalisms, it is hermetically sealed: you can never convince a Freudian it isn't all about sex, or a bible thumper that it isn't all about God's word.
I always find that a little depressing with libertarianism, as there's enough useful material there that I hate to see fanatics turning people off to it. There's a giant difference between "an important function of government is" and "government's sole duty is". The latter is appealing to people looking for simple answers to complicated problems, but is actively off-putting to everybody else.
I understand you don't think you're an anarchist, and, for a different reason, I'd even agree. I think the step-over-the-dying school of libertarianism would turn out, in practice, to be indistinguishable from the sort of chaos that people who don't know any actual anarchists think when they say "anarchy". (The interesting sorts of anarchism, like what the anarcho-syndicalists were pursuing, depend upon a human moral sense. Which, bringing this back, include compassion for the ill.)
The reason things will fall apart lies in another gap in your thinking. Parents are the most obvious thing a child depends upon. But try telling a teacher or a grandparent or a cop or a social worker or a neighbor or an aunt that they don't matter, that they don't have an impact on the kids they deal with. It takes, as they say, a village. Or, if you'd like a richer society, a lot more than that. You'll of course wave that away as inconsistent with your chosen theoretical framework. But that you can't perceive the value in something doesn't prove that it's valueless. It only shows you haven't bothered to really understand it.
I always find that a little depressing with libertarianism, as there's enough useful material there that I hate to see fanatics turning people off to it. There's a giant difference between "an important function of government is" and "government's sole duty is". The latter is appealing to people looking for simple answers to complicated problems, but is actively off-putting to everybody else.
I understand you don't think you're an anarchist, and, for a different reason, I'd even agree. I think the step-over-the-dying school of libertarianism would turn out, in practice, to be indistinguishable from the sort of chaos that people who don't know any actual anarchists think when they say "anarchy". (The interesting sorts of anarchism, like what the anarcho-syndicalists were pursuing, depend upon a human moral sense. Which, bringing this back, include compassion for the ill.)
The reason things will fall apart lies in another gap in your thinking. Parents are the most obvious thing a child depends upon. But try telling a teacher or a grandparent or a cop or a social worker or a neighbor or an aunt that they don't matter, that they don't have an impact on the kids they deal with. It takes, as they say, a village. Or, if you'd like a richer society, a lot more than that. You'll of course wave that away as inconsistent with your chosen theoretical framework. But that you can't perceive the value in something doesn't prove that it's valueless. It only shows you haven't bothered to really understand it.