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It would also be extremely regressive...

I don't buy the word "regressive" in tax discussions, too agenda-loaded ; )
Taking here the notion that consumption is a good first proxy for wealth,
regressive and progressive taxation schemes are more neutrally described
as taxation proportional to wealth versus geometrically varying as wealth.
"Proportional to wealth" sure sounds a lot less loaded than "regressive".
(nice analogy to the history of the word "bolshevik", meaning majority,
the name chosen for itself by the minority party of the time)

In any case, it's no biggie, since there are lots of things in the income
tax system which make tax a nonlinear function of income, and those parameters
could be tweaked to keep the non-linearity of taxation if that's what one wants.
The advantage of sales tax (usually combined with a credit for low
income households—a linear function need not pass through the origin)
is that it is a tax which is extremely efficient. It doesn't discourage investment,
employment, or savings, and doesn't cost that much to collect in an advanced economy.
It collects the most money for a low cost and minimal economic distortions,
depending only on the power of the lobby groups who try to get exemptions.
Economic distortions explode rapidly, so it's generally best to have
a hard line with no exemptions beyond unprepared food.

and dampen demand in the middle of a recession/depression so it may be a really disastrous idea...
I agree that's a big concern; the UK is a prime example of attempting
to lose weight by decapitation. But there's nothing to say when it has to kick in.
Also, as mentioned it's an extraordinarily efficient way to raise tax,
dampening economic activity as any tightening does, but in the most gentle way.
Indeed, the argument raised against it most often is that it works
so well that governments can raise it too easily without breaking things.
At some point I imagine the US government will have to stop spending
$100 billion more a month than it's taking in; might as well start planning at least.
The introduction in Canada was unpopular to say the least, but it fixed the finances rapidly.
People still hate it, but it's now mixed with a reasonably well earned
smugness for having dodged the bulk of the recent unpleasantness which
was in part due to good regulation, but largely on strong finances.

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