A lot of people cannot miss work. There are a lot of families in which both parents (or THE parent) works, and a lot of jobs at the top and bottom of the spectrum do not allow for generous personal/sick days. At the bottom/low-paying end, there just aren't benefits and people are, sadly, replaceable. At the top end, certain professionals have tremendous responsibility and someone else cannot just step in/things can't be postponed, and frankly, you just don't make it to the top if you're taking days off with any regularity for sick kids (I'm thinking trial lawyers, oncologists, top business executives, etc. here). In between, there are jobs that allow some flexibility - teachers, administrators, many unionized jobs, but there are a tremendous number of families who do not fall into this category.
In my previous career (well paying, professional), I could not use sick days for a kid's illness (and it was a small company, yes, they would have known). If my kid were hospitalized - yes. If my kid felt lousy & couldn't go to school - no.
My parents could also not miss work for sick kids. If there were a childcare issue, we went to work w/my mother.