Typical provisions about how you can theoretically create a consumption tax to get around these issues, but what they are saying is the empirical truth. Consumption (or sales) taxes are inherently regressive. This means they disproportionately affect those who earn less money. When you increase a consumption tax from say 5% to 10%, the brunt of the real life effect will be on individuals who have less discretionary income. Those individuals spend more of their income on basic necessities therefore increasing the cost of those basic necessities will have an undue impact on those individuals.
Beyond whether the sub top whatever percent spend more money, since that is an empirical question. If someone earns $20k per year and spends $15k on basic or close to basic necessities on a tax rate of 5% on those necessities (~$14,286 pre tax), when you bump the tax rate to 10%, they now spend ~$15,714 on those same necessities. That's over $700 that the individual cannot now spend toward investing in their future or building a bankroll to insulate themselves from poor rolls at luck in the game of life.
To my non-trained eyes, there are two ways of challenging this accepted wisdom. One empirical question to challenge this accepted wisdom would be whether growth in what is considered basic necessities scale at such a rate that it will balance out the hit of the tax hike. This seems unlikely to me. Yes, the richer spend more on let's say food than the non-rich, but does someone who earns 10x the $20k earner spend 10x on food? Unlikely. The other empirical question that could challenge this accepted wisdom is whether spending on non-necessities for the richer scales up at a rate that would make up for the increase burden on the poor. I doubt this is the case either, but there are plausible stories one could concoct to lend it credibility. If you have more discretionary income, you're more apt to buy a new gadget or eat out a more expensive restaurant than you would otherwise be.
IMO, neither of those empirical questions adequately address the moral question of what is the impact on the poor. Even if it were the case that the person who earns 10x spends 10+x on food, that isn't something the state should really care about. If Joe Millionaire has to switch from the $100 bottle of wine to the $50 bottle of wine it doesn't rival the moral concern the state should show towards Joe Working Poor who is out $700 on the literal basic necessities they need to survive. When you have situations where the state decreases the ability of those struggling to succeed in life, then the state isn't living up to its obligations. But this is admittedly a moral concern, not an empirical one.