Quiet time at my house is not negotiable. After lunch, for at least 2 hours. It is usually from 12;45 until 3. If a parent was asking to cut out nap for an under 3 year old, the most I would be willing to do is wake them up earlier. They still nap, because they still NEED to nap. Past the age of 3, I still require them to lay down and rest for an hour. After that, they may get up and play QUIETLY with a variety of quiet activities I have out for them. I only have one 4 year old that will not sleep. She picks a movie and lays down quietly. The others still fall asleep.
We talk all the time about how resting our bodies helps us to grow.

And I might lose my shizzle if a parent ever questioned me on the need for a 2 hour "break". Most days I am trying to frantically finish cleaning/prepping/planning for the daycare in the final minutes of quiet time!!