Because it would seem to me that consumption of low-income earners will trend toward below-the-median while consumption of the wealthy will trend toward above-the-median, giving you an additional handle to make this taxation progressive.
IMHO it’s easier to construct a “fair” tax system on the income side than on the expenditures side, provided you count all income equally. Currently income from labor is usually taxed higher than income from investment, and that’s not fair.
The difference can be explained by this completely made up example: A steel mill buys iron ore for $1 a kilo and makes steel of that. A nail factory buys steel for $1.50 a kilo and makes nails of that. A distributor buys those nails wholesale for $2 a kilo. A hardware store buys those nails from the wholesaler for $2.50 a kilo. A contractor buys those nails from the hardware store for $3 a kilo. The subcontractor bills $3.50 a kilo for those nails. The general contractor bills you $4 a kilo for those nails.
With VAT you/the general contractor/all businesses involved pay taxes on a total of $4.
With a transaction tax, it would be paid on $17.50.
But the above is a simplified example. In the real world there are probably a lot more businesses (each specializing in their own niche) and therefor transaction involved in getting that nail into your wall.
If you have a product that goes from mine to mill to factory to wholesaler to retailer to consumer, the tax is paid five times. But if the same company owns the mine as operates the retail store, it's paid only once.
That's an insurmountable advantage for vertically integrated companies, so no others remain and tax-wise you end up with the same result as sales tax or VAT (i.e. the tax is paid on the total final value) except that you've needlessly destroyed every non-vertically integrated business.
That is the problem that VAT solves, by giving longer supply chains the same tax treatment as vertically integrated corporations.
One of the most important things to understand about tax discussions is that there are two broad classes of "rich" -- high paid salaried employees vs. wealthy investors.
When you see claims like "the top 20% of people pay most of the taxes", that's mostly the high paid salaried employees. Cardiologists making six figure salaries pay high tax rates, and there are a lot of doctors and lawyers and engineers in the population, so they pay most of the taxes.
When you see claims about rich people paying low tax rates, that's corporations and wealthy investors hiring accountants to minimize their taxable income.
The distinction is really important because it means the problem isn't marginal rates, it's the complexity of the tax code which allows people with large fortunes to game the system. A simple VAT with some kind of dividend/UBI to make it more progressive would eliminate most of those games. It would also mean that individuals wouldn't have to file tax returns at all, which would save hundreds of millions of man hours every year.