You're mixing income tax with consumption tax. If you want to tax income, tax income. But if we're taxing consumption, then those who consume more pay more than those who consume less, and those who consume least because they have the least to spend pay the least in taxes because of the baseline exemption. The upper middle class guy who's busting his butt to pay off his student loans, and who saves as much as he can, is not going to pay a disproportionate amount in taxes. (Or are we going to tax his student loan payments as consumption, even though he paid consumption tax while living on those loans? What about deposits in a savings account, or stock purchases? If we're going to do that, we may as well just call it an income tax, because that's what it is.)
If he pays off his student loans and still chooses to live modestly, he continues to pay a low tax rate. If he instead decides to start living large, then he'll start paying more in taxes. Either way, he essentially chooses his tax bracket, because he chooses every day what to buy, and how much to spend on it. This is especially true if we're giving him a front-loaded exemption on expected costs for rent and groceries. In other words, we're not taxing him for living, eating, and having shelter, and we're not taxing him for working and earning money. We're taxing whatever life style he chooses above and beyond the baseline. This tax is progressive in that people who choose to live modestly or who cannot afford to live extravagantly pay very little in taxes. Those who are able and choose to live extravagantly pay much more in taxes. Yes, you could have a billionaire who pays no taxes because he chooses to live in an efficiency and drive an '86 Yugo. That's only a problem if you believe that the government owns all income, and is naturally entitled to its "fair share," because class warfare or whatever. I prefer the tax theory of take from people the very least necessary for government to function. And I suspect there would be very few billionaires living tax free under this system, because it has an actual lifestyle cost to them. The only cost now for billionaires to live tax-free is they pay their accountants and lawyers $900/hour to get creative with shell entities.