(I'm aware that people with very low incomes and no paid holidays at all, may not be able to afford that. But that situation should be illegal in any modern, wealthy country. I guess the answer to the question above may indeed be "yes" in some cases.)
Never being able to take a day off for anything at all is incredibly harmful. People used to fight for these rights. What happened?
As for what happened, the US isn't highly unionized outside certain regions and trades. Everybody else has next to zero legal protection. White collar workers typically get some leave simply by virtue of having skills that are more in-demand. And the labor movement largely allowed conservative, anti-labor factions to cast them as evil socialists. In the US, "liberal" has long been a bad word.
Everybody got convinced that a) those rights will be used by those people who obviously don't deserve it and b) those rights will make life harder for them when they become billionaire business owners.