My experience is nasal cannula patients are never asked to be in a prone position. It's not something I've ever seen a doctor order and it's not something that our beds on regular patient care floors are made for. Many, many patients we see in the hospital are older, have arthritis or bad backs and have difficulty finding comfortable positions at all. Sometimes the best we can do in terms of position is highly encourage them to sit up in a chair.
In other words, it's a lot easier to prone a vent patient because they aren't going to whine about it.
I absolutely see the physiological benefit. It reduces the pressure on the lungs by the heart and fat tissue and allows more lung tissue to be ventilated. There are some other benefits as well.
For anyone wanting to read about it, here's one paper:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6026253/