It for sure problematic for professional photographer, but I also see it from the prospective that if parents doing any sharing of pictures from your page (even just a dad linking it to the grandma or something) then you have the problem that those pictures can never actually be deleted. So if you have pictures of all the daycare kids and a family leaves it can make it impossible to get rid of those pictures off the Internet. There is a certain level of loss of control with social media (even with the use of security settings) as opposed to posting pictures on a personal website with password protection. You can even make it impossible to have pictures downloadable or able to be copied using a personal website.
I have a social media policy for my daycare where parents are not allowed to post pictures online (facebook, etc) or share the pictures with anyone if it has anyone other than their own child in the picture. Whenever I email pictures I always have this reminder accompany the photos.
I think the idea of using a private Facebook page for everything other than posting pictures of the kids is a good idea.