I would have no problem seeing an NP for something as simple as a physical. A physical exam isn't rocket science. If you need a more experienced eye after that, they can always refer you to their physician colleagues, and I am a physician.
I think a basic rule of thumb that a lot of people seem to either be maybe not aware of or not willing to do is; if you're unhappy with how someone is managing your care, regardless of who they are, see someone else. No one says you're beholden to one specific person. See another NP or PA or physician.
Do I disagree with the laws passing in several states that allow PAs and NPs to practice independently. Absolutely. I don't think there are any circumstances in which they shouldn't be under a physician's direct supervision. That being said, a first year med student could handle a general physical.