Many? Most? People earning (say) $500k+ dodge their income tax, legally and illegally. There's a whole industry of it. Yes let's clamp down on that as we've been trying to across the world for decades. Not likely to eradicate it by next year though, right?

So you tax consumption at a flat rate /in addition/ to income tax. You ensure the people earning less get a tax break or a transfer payment increase to cover the consumption flat tax and then some.

All those wealthy people are now paying that base rate on their consumption in a way that is basically unavoidable.

So for your progressive taxation, the initial bracket cannot be avoided. People in higher brackets still should pay more.

By using consumption to tax the initial bracket the poor get an increase in after tax income. The rich (on average) get a higher tax bill.

Yes it depends on the modelling and getting the implementation right as all tax regimes do. Yes it is progressive.

When you see consumption tax as necessarily regressive (as I did once) you are missing the most important thing about them which is they really aren't. They're the best way of getting a big tax revenue increase at the expense of those who cheat. I like that, myself.