I read your articles. First, the income tax is barely progressive anymore. The slide toward flattening it began in the early 1980s and continued on through today. So I would not consider that an assumption anymore- certainly not the progressive marginal rates we had from the 1950s through the 1970s.
A sales (consumption) tax is absolutely regressive. No assumption there at all. Your title "Consumption Taxes are Progressive" is not factual to the NOW status of sales taxes- only to the one you are imagining implemented.
Taxes are not the tool for controlling inflation. Inflation is complex and not solely derived from spending money. Trying to use taxation to control inflation is using the WRONG tool!
I think you have the Theorem of Optimal Taxes framed incorrectly. According to a paper by Mankiw, etal., "The standard theory of optimal taxation posits that a tax system should be chosen to maximize a social welfare function subject to a set of constraints"[1]
Trying to make sales taxes progressive with rebates is an interesting idea, but as usual the actual implementation is the issue. Trying to provide rebates annually via one's filings with the IRS doesn't even come close to offsetting the pain at the checkout line day after day. Trying to provide rebates more frequently such as quarterly or monthly seems an impossible feat logistically. Either way, forcing taxpayers to maintain receipts and records to submit for rebates is onerous at the very least!
The ONLY mechanism I see which could effectively offset your sales tax idea is Universal Basic Income checks sent out to all citizens at the dollar value arrived at via a progressive table based on their income. And we know that Republicans will NEVER go for UBI.
Current operation is all done via the Federal Reserve- if inflation rises, tight money ensues, thus crunching the economy, thus throwing people out of work. A mild level of inflation is needed for a growing economy. The FEDRES has dual mandate: 2% or less inflation and full employment at 4% unemployment rate. But the FED cannot do both effectively.
But UBI and / or a Federal Jobs Guarantee WOULD help control our economic cycles (and in a roundabout way, control inflation). The Fed could focus on the money supply and interest rates and not worry about the unemployment level because there would not be unemployment. Stable income and employment would smooth out the business cycles.
[1]
https://scholar.harvard.edu/files/mankiw/files/optimal_taxation_in_theory.pdf
