Also, even if you’re a new mom who thinks it should be private, the lack of easily-accessible private places kinda severely restricts your movements. And even some more-widely-available private places (port-o-lets) are unpleasant enough you’d really rather do it in public.
So basically moms who think it should be private use a little baby blankie or something to cover up, but still do it in public. Moms who think there’s nothing sexual about eating cover up with a baby. But not doing it in public at all? That’s not really feasible.