When I was teaching, my kids napped until they were at least 4. If by 4 they were consistently not napping, they could have quiet time. But they at least had to lay down and rest for a while. Most of the time they'd fall asleep for a bit. But this was a school setting...so they were pretty tired mentally and physically by nap time. I even had 5 year olds that would occasionally want to lay down and rest.
Eventually toddlers want to fight a nap because they don't want to miss any of the fun you might be having without them. If she falls asleep after fighting her nap...she clearly still needs a nap! 4951