A lot of people don't realise inflation is essentially a stealth cash wealth tax. It applies to savings, debt, dollar-denominated contracts, etc.
The poor don't hold debt. "I live in a nice house that's still owned by the bank" is not poverty.
And you might find that even many of the rich (who have far more in assets than they have in debt or cash) will still have more debt than cash, because while investing on debt is generally considered stupid, investing on debt that could be fully cleared by the the object invested in (house/land) as collateral is the exception. People rich enough to buy houses for renting out rarely pay them in cash. The winners of inflation debt decay are not who you think they are.
I would think that the poor have no cash… that's why they're called "poor" after all.
The bottom 50% of income earners can barely cover the 'necessities' (housing, food, transportation, healthcare):
* https://ofdollarsanddata.com/the-biggest-lie-in-personal-fin...
They have contracts denominated in cash—for example, their wages from employment. That's where inflation tends to hurt the most since wages tend to trail behind inflation (or deflation). And of course being "poor" doesn't imply that you literally have zero savings, though you probably don't have enough to be worth the hassle and expense of a brokerage account to invest in stocks, ETFs, or mutual funds. For small amounts the transaction fees alone would be more than the gains.
Regarding the article you cited, it occurs to me that the authors never mentioned how long any given household remains in a particular category. If I took a year-long sabbatical from work, for example, then I would end up in that "lowest 20%" group with zero income while I lived off my savings, but that doesn't mean I'm experiencing any kind of financial difficulty. The same goes for students still receiving support from their parents, or for anyone who is retired and living off of a lifetime's worth of investments (though probably not pre-tax 401(k)/IRA, depending on the study methodology, since these distributions are generally considered "income" for tax purposes). "Lowest 20% by income" is not a fixed group. This is apparent simply from the fact that expenses cannot exceed income indefinitely; eventually you must either increase your income, at which point you are no longer counted in that statistic, or else decrease your expenses. But the idea of a shifting group of households which temporarily earn less than they spend paints a very different picture than the one the article implies.
The benefit is that if the creditors (mostly upper classes) refuse to forgive the debt then you don't need an angry mob with pitchforks to cancel the contract (revolution).
Yes, bigger down payments suck but that is mostly a zoning/housing supply issue.