> But I have seen nothing to suggest that the tax-hike crew have any good ideas about spending either. Their idea seems to be "let's just be Denmark”.
I've seen none where this is the case.
> And the issue with progressive systems is that all other things aren't equal.
You can compare situations where things outside of the tax system are, if not perfectly ceteris paribus, at least more comparable than in normal country-v.-country comparisons, like comparing the US before Reagan's tax burden shift to the US after. And when you do that, suddenly progressivity and inequality become opposed. It's only when progressivity is offset by something that mitigates it's ability to drive down inequality that it doesn't have that effect.
> Progressive tax systems don't work.
But they do. The fact that they can (and in the case of the US absolutely do) have their effects offset by larger effects of other aspects of policy that are directed at opposing ends doesn't mean they don't work, it means that if you want reduced inequality, you can't crank those opposed policies up when you crank up progressivity, you need to at worst leave them alone or, better, dial them down.
> The idea of upward and downward redistribution also sounds like something beloved of theoreticians.
It's simple fact if you take money in and send money out, you are either sending the average dollar back to someone who has greater, equal, or less wealth, income, or whatever measure you are concerned about than the person the average dollar came from.
> as an example: the idea of a "single payer" health system is just preposterous
That isn't really an example that clarifies and supports your conclusion, since it is itself an unsupported and equally controversial conclusion to the one it is offered to support.