I feel your pain. I am very anal about socks.
I don'twant grubby, sweaty little feet leaving sweat and dirt all over my hardwood and carpets where my own family lives. My own kids play on the carpet and floors and I like to keep it clean for them. I don't find it hygienic and a lot of indoor playgrounds and McDonald's Playland ask for socks for hygienic reasons.
I ask kids to wear socks and I have written it right into my contract now.
I have parents tell me that their kids don't want to wear socks and I just remind them that they are a requirement here because of sanitary reasons and because it can help prevent slivers from the park woodchips or any injury if they step on a toy or pull a toenail.
In your case I would be watching that child like a hawk and put the sock back on a hundred times if that is what it took for her to understand that socks were needed at daycare.