Is this really true? There are millions of parents who are unreachable while working. A surgeon isn’t going to be able to leave in the middle of surgery to pick up their kid from child care.

My kid got sick at daycare one time when I was over an hour away. They just had to stay there while I worked my way back.

It happens, and it is handled normally.

I don't think that's a counter example. Our day care requested sick kids to be picked up within an hour. A single late pickup of a sick kid due to traffic/distance would be handled normally. An unreachable parent who turns off their phone and is extremely delayed, especially on multiple occasions is a very different thing.

When we looked at in-home child care, one of the options was a nanny who would care for kids even when the kids were sick. So I'm sure the rapid-pickup-of-sick-kids policy isn't universal. However, our day care had that policy and we made sure we knew who was "on-call" to get kids when important meetings or work travel impacted our availability.