Ok, I feel the need to answer this question in defense of the preschool teachers/ daycare. (I will say that I have NOT been really impressed by many of the preschools here in the state of Florida, but in general this is an answer to the nap time question)
I had a liscenced home daycare/ preschool in Massachusetts for 11 years, and I taught at an upscale preschool for several years as well. The 3 hour naptime is most likely the time that they allow on their schedule for EVERYTHING, after lunchtime, from cleaninig up tables, washiing up the kids, brushing teeth, changing diapers or using the potty, getting cots/ napmats set up, (which hopefully was done while the kids were eating), and reading a story or 2 to help settle the kids down for their rest time. Also, they probably have an area set up for the kids who don't "sleep" where they can lay quietly and read or watch a video. Most of the time, there are children who require a teacher to sit next to them while they fall asleep to quietly and gently rub or pat their back , and calm them for a few minutes to help them settle. Now, do this several times over with however many kids are in the classroom, and there is most likely the better part of your first hour with the clean up and prep time. The teacher will keep track of who fell asleep first, and will be sure to wake that child first if they don't wake up themself. This again is a process, lilghts on, gently going around the room and touching their backs to wake them, etc. Some of the kids may need a little tlc or cuddle time, depending on how they wake up. Also, the diaper changes and potty trips are going to happen at this time again. Trust me, as a provider... YES we do need this "down time" at this point of the day. It's NOT because we are lazy or because we don't want to interact with your child anymore. We are usually spending that time doing paperwork, like your daily report for you to take at the end of the day, etc. Also, it is sometimes the only time of the day when we get to eat OUR lunch or have a few minutes peace. We still do not really get a "break" because we are with your child while they are sleeping. Law states that we have to be. Not like at home, when you can run to the garage to throw in the laundry. We must be in the room. Another thiing to consider is this..... your child may not seem tired enough to nap at home, but do they play with as many children at home, or have the same hectic schedule while at home? I seriously doubt it. I have had several parents over the years who have told me "oh, MY child has not taken a nap in years! He/ She will NEVER sleep in a room with all of those other kids." I had a tough time controlling myself at pick up when I had to let them know that their child was the first asleep, and the hardest to wake up. It really can make a child tired, more so than usual. They play hard, WORK hard on learning, and get overstimulated. The nap/ rest time is for them to recharge. Without it, you would not like they way your child would act at the end of the day! I have never had a parent complain and tell me that their child wasn't sleeping at night because of their taking naps at my daycare, and I had ALL of my kids take naps. They ALL slept, even the 5 and 6 yr olds. I never told them they had to sleep, just to take a quiet time. They fell asleep on their own. I also have never had an unhappy parent or child. I still stay in contact with all of my "kids" some who are out of high school at this point, and it's wonderful to talk to them when they call or get cards when they write. They loved coming to my daycare/ preschool, and were never upset by the nap/ rest time, so please don't let that be the thing that makes up your mind if the school is great in every other way. I had kids whoo cried when it was time to GO HOME. Most of my parents were ok with this, and even said they would rather that they were upset to leave, than upset to be left there. At least they knew they were happy and well cared for. I thought it was a loving thing to say. (one that I wasn't sure I would have been able to say myself if it had been my child) If you are really worried, talk to the preschool more, the other parents, and stop by to check things out. Please be prepared though, that if you stop by DURING naptime (with your child who is awake I mean), you may not be the favorite parent of the preschool/ daycare teachers. They just want to do their job and do it well. (teach your child and care for your child.) I really hope that you get the answers that you are looking for and need and find the best care for your child. That is what is most important for you and your child. Good luck!