Part of the worry is that even for completely non-essential jobs, managers will say "you can still send your child to school so I expect you to come in and work

Part of the worry is that even for completely non-essential jobs, managers will say "you can still send your child to school so I expect you to come in and work". "Schools are closed" is a much simpler message, and I imagine the vast majority of doctor parents can arrange for a non-doctor parent (from another family) to provide their childcare.