An afternoon nap is a healthy choice for everyone. Yes, even us adults would benefit from 40 min to an hour to help us be fully cognitive for the rest of the day. The only time our body heals (rest and repair) is when we sleep. Judy, as usual, hit the nail on the head. A child that stays up to 11 is an over tire child and good bedtime parenting will result in the child going to bed and sleep on time.
A few of my daycare kids I know could easily sleep 3 or more hours in the afternoon due to being up till late evening due to family sports and other activities. My nap time is 12:30 - 3:00. I often do have to wake the children up.
That said, I agree with Kelly P, find another daycare that will suit your nap opinion or work with your provider and let your child rest at daycare.