I can understand the frustration on your end (the parent) but I think a lot of us caregivers are frustrated with the high number of parents that request no naps but have no sleep routine, no sleep expectations and have no control over their child's sleep. It can be a touchy subject for all...but this job is hard and having to be on our feet the 10hr day because "those" parents whose kids are not sleeping at home (with or without nap and for reasons completely unrelated to naps) believe everything will be magically solved by us forcing their kids to stay awake (you know, the kids that are asleep within 10seconds of lying down because they are so exhausted).
I don't doubt many kids don't need that nap, are getting plenty of sleep at home and can function perfectly without any nap. BUT I do believe we have all seen that the number of kids that are not sleeping at home, are not functioning due to lack of sleep far outweigh the ones who are. It is those children that often make us clamp down on the nap rule...for everyone's sanity.
The kids with good sleep habits would be able to just hang out on their mat with a couple books being still and quiet (and not fall asleep within a short period of time). In this case there would be no issue over the nap or no nap because the caregivers is still getting their child free rest time even if some kids are awake on their mats.