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I would say classical liberalism of yore is closer to libertarianism today.Of course it is. But that's not what "liberal" means anymore in everyday speech in America.
I'm well aware of Isaiah Berlin's delineation of negative and positive rights, of Robert Nozick's defense of property rights, and so on. I'm extremely well-versed in libertarianism.
That doesn't make it any less extreme. Governments have redistributed in one form or another since time immemorial through taxation. Nobody succeeds solely on their own -- we benefit from roads and schools and libraries and hospitals. So of course we take things from others (through taxes) to help everyone out, for the greater good. We're all in this together.
And here's the thing libertarians ignore: neither Locke nor Nozick ever produced any convincing justification for a natural right to property, because there isn't one. A general idea of property rights is a useful thing, but not an absolutist one. My labor is at least 1,000x more productive than it would otherwise be without society around me. Surely then I don't deserve to keep the full extra 999x just for myself? Surely I owe some of it back to the society that helps me? One way of framing this is social contract theory, from Plato to Hobbes to Rawls.
In addition, the way you characterize the modern conservative/liberal divide is inaccurate. It is abundantly clear that modern liberals are far less hawkish and far more in support of civil liberties (free speech, right to vote, equal treatment, etc.) than modern conservatives. To characterize the differences between the two as "farcical bickering" is a hugely irresponsible, counterfactual, and I would argue ultimately immoral position to take. You have to be blind to modern American to say otherwise.