That's why the quote explicitly says "Instead, impose a consumption tax, designed to be progressive to protect lower-income households." Now how that's calculated I'm not quite sure, maybe they'd pull up your income details at every point of sale.
This argument kind of illustrates why consumption tax is better. It's easy to advocate "lower taxes for everyone!" giving rich people most of the benefit, but it's much harder to advocate for "lower yacht tax!" without pissing off a whole bunch of wage workers.