>Given a system like that I'd be curious what the numbers might really look like. How high a tax would we need? What would the actual tax burden look like for different amounts of cash-back?
It seems like the math is fairly straightforward, but dependent on how much money you need to raise. The big question is to what extent you would want something like that to displace other taxes. If you wanted to displace all other federal, state and local taxes then a sensible rate would likely have to be in the nature of 20-30% (depending on the size of the exemption and how much money the government is to spend).
>Could we replicate something similar to the progressivity we have now?
It seems to me you could achieve an arbitrarily large degree of progressivity by playing with the size of the exemption. In the extreme case you pay everyone something like $50,000/year and then have an extraordinarily high tax rate, but then you get a different kind of distortion where people quit their jobs because they can live off the tax rebate.
On the other hand, having a substantial unconditional rebate (not that large, but say $5000-$10,000/year) would eliminate the call for many need-based programs, because those in need would then have that money with which to buy food and shared accommodations, etc. That would significantly reduce government expenditures for those programs and allow such a large rebate to be had without the need for a prohibitively high tax rate. (It would also eliminate several redundant government bureaucracies dedicated to administering now-redundant need-based programs.)
> Why are goods taxed but not services? I've never been clear on that.
I think it's jurisdiction dependent. But as to why, it's almost certainly only because that's what has been successfully lobbied for by someone. There isn't any sound economic rationale unless you want to encourage the purchase of services over goods for some reason, at the cost of exactly the sort of distortions you're talking about.