I’ve certainly heard a few variations of this one, many times over.
There’s a terrible fear that babies will just pop out from their walking, moving mothers, and go bouncing on the floor.

Babies are really slippery. I was surprised at how slippery the baby was the first time I helped catch a baby birthed in the standing postion. But two hands pretty well takes care of the “wet fish” situation.

I believe most women birth crouching, not standing upright, and generally they birth close enough to the floor that its NOT a problem if the baby drops.

Also giraffe’s birth completely standing and their baby falls. Giraffe baby deaths from falling are unheard of.