You can with many nurse practitioners (and maybe physician assistants, but I've had no experience with them) at places like minute clinic (http://www.cvs.com/minuteclinic/).
I've gone to a similar place that's in my office for some minor routine things, and it's been cheaper and easier to schedule than a proper doctor visit.
They certainly do have an important role to play, but we need a lower level medical professional that can accept appointments and perhaps write a limited set of prescriptions and handle treatment of basic ailments.
One shouldn't need a masters for the 'oil change' of medicine, just as one needn't be a registered engineer to change an air filter.
The last time I needed a basic physical, I saw the PA. She ordered blood-work and reviewed the results with me. I'm sure one of the physicians signed off on everything, but as far as I know, she did the work.
Likewise, the last time I had the flu, I made an appointment with one of the PAs. She did everything, with the physician just signing off on the prescription at the end.
Post-surgery, my follow-ups were with PAs or NPs, not the physician. He did drop in to say "Hi." but that was about it.
So I think that varies from state to state.
[Anecdote warning] When I was in grad school, at least, I was able to directly book appointments at the student health center with PAs, MDs and DOs (perhaps a university-run health center is different, somehow?). I also don't recall ever facing difficulty having a prescription written.
My understanding is that a PAs can't open their own practice, but that several PAs can function more or less independently under the supervision of one MD/DO principal.