Earlier quoted context omitted.
It could be coupled with a hefty UBI. No need for means-testing. If everyone got e.g. $10,000/yr, that would completely offset VAT for people who don't buy much. People who spend millions every year wouldn't even notice it.
I'm not opposed to the idea of UBI, but it doesn't really solve any problems here, it just adds massive political and logistical complexity that would essentially doom any possibility of reforming the tax code.
The initial, flawed response to this issue would be to construct some "massive political and logistical complexity" in order to track everyone's income and spending and family situation and lots of other stuff too and calculate their VAT refunds based on some formula. The much simpler solution is to just give everyone the same amount of money. Poor people will spend some portion of it on sales taxes, and they'll use the rest for other purposes of their choosing. Slightly richer people will spend all of the UBI on sales taxes but will come out even. Slightly richer people will be able to offset some portion of their sales taxes. Really rich people won't even notice they got a UBI.
Perhaps you really meant that "massive political and logistical complexity" is required to get anything through the legislative process? After all, the more complicated it gets, the more places lobbyists can hide loot for their employers.