> As a final thought, the idea of using a VAT to finance a basic income is nice, but it doesn't help against wealth inequality, because poor people generally spend a much higher fraction of their disposable income on stuff on which VAT is paid.

Using VAT to finance a basic income is only useless for redistributing income if income is already well distributed[1]. Otherwise, rich people will pay the majority of it (regressive or not) and poorer people will get better off. You are right that there's always a certain income that (if rich people do really invest it all) the combination will be regressive, but it can always be made big enough that it does not matter.

Also that's ignoring all the other benefits of both the VAT and basic income, in that they are cheaper than the alternatives to administer and easier to control, offer a safety net that actually works, incentive risk taking, creates no barrier for improvement at any level...

[1] Of course, the actual numbers will depend on the VAT rate, and the amount redistributed.