I'm not sure lack of healthcare and low wages _is_ the main issue[1]. As the parent comment points out, it seems like that would lead to a pretty different pattern of this phenomenon. It seems to me that there's a couple broad categories that can lead to paycheck-to-paycheck living:
1) Poverty, at the level where spending on a reasonable floor of basics (food, shelter, education, leisure) leaves little for savings. This is a resource constraint, and even a perfectly optimally-run household would end up living paycheck-to-paycheck.
2) Severe exogenous financial shocks that exceed whatever buffer you were able to build, and an inability to adjust consumption downwards due to sticky commitments or psychological reasons. For lower-middle and middle-class households, this is possible simply due to bad luck; one thing the US economy is pretty bad at is providing a solid way to derisk tail risks, the obvious example being healthcare. This is naturally less common the more severe the shock, and irresponsible financial management can be a contributor in some of these cases (ie not saving an emergency fund, etc).
3) Consumption rising to meet one's income. The resource constraint is irrelevant here, as above the poverty level, this is primarily about hedonism and jockeying for status. The big caveat here is that people tend to short-circuit cost-benefit analyses when it comes to their kids: neighborhood safety and public school quality can lead to people substantially (and understandably) overextending themselves wrt housing costs. I'd caution against leaning too blindly on this mitigating factor though, as there are lots of differences between living modestly in a good school district and living generally beyond your means.
There's a degree of freedom around consumption that's likely a lot more significant than your comment assumes; this seems to follow directly from the fact that someone living beyond their means at percentile X would substantially improve their financial security if they spent as much as percentile X-10 (or whatever). For all but the lowest percentiles, this is completely feasible, and yet these low-savings studies consistently find a much larger swathe of people in these categories.
The model that makes the most sense to me is that, excluding the lowest quintile, the habit of clamping consumption to income is one of the biggest factors in our low savings.
As mentioned above, the US systemically tends to put a lot more risk on the individual than a lot of societies do; you can be better off if you manage this responsibly (and aren't in the lowest income brackets), but financial illiteracy is IME rampant, even among generally well-educated people.
[1] Lack of access to quality education likely is, but through the mechanism of low numeracy/personal finance skills/critical thinking skills.