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But now Cruz comes along and says I also won't charge income tax. I will charge a VAT. She is now 20% worse off than she was.

The tax on businesses, which is effectively a VAT, is offset by the elimination of the payroll tax. For some businesses this will be a wash, for others a boon, and for others, a cost that will be passed on to their customers.

The analysis from the Tax Foundation shows the overall effect to be a boon to the economy:

According to the Tax Foundation's Taxes and Growth Model, the plan would significantly reduce marginal tax rates and the cost of capital, which would lead to a 13.9 percent higher GDP over the long term, provided that the tax cut could be appropriately financed.
The plan would also lead to a 43.9 percent larger capital stock, 12.2 percent higher wages, and 4.8 million more full-time equivalent jobs.
On a static basis, the plan would cut taxes by 9.2 percent, on average, for all taxpayers.
Accounting for economic growth, all taxpayers would see an increase in after-tax income of at least 14 percent at the end of the decade.

The world is awash in capital. There is no lack of it, and I am not happy about continual efforts to shift the tax burden off of super high income earners because of the problem of who it shifts the burden on to. And that is me and every other upper-middle-class taxpayer - because that is where the money is.

I don't need another convoluted hypercomplex analysis from Ted Cruz or the Tax Foundation explaining how I will be better off when I pay more taxes.