Physios who are qualified und Chartered physios can work without supervision. It doesn't mean however, that they can "fix" everything just like that in every patient they meet. Is she newly qualified or still a student? Is she new in this particular situation?
I would expect a physio or physio studentto be bright enough, if not getting any progression or success with a problem, to talk to fellow physios for advice.
And even long qualified physios can't "fix" everything. We can often improve and manage a case using a wide selection of modalities available and by teaching the patient to manage and help fix it. You don't say exactly your diagnosis is and what part the doctor played in explaining it to you before referring you to physio. Does your doctor know of your frustration for lack of progress, it's been a long time already.
Speak to your physio about your impressions of lack of progress. See what answers she come up with. Reading your "not physio bashing" I can't understand why you are going to her still or haven't talked to her about it. She must notice what your thoughts are. Maybe she is less competent than others. In all professions, some have more talent some have less, to grasp a problem and deal with all sorts of clients. But if she's qualified she can work without supervision. You say you are in military. Your profession demands alot of your body and knees. Maybe too much? I can't say as there is not enough information about your diagnosis; state of cartilage and joint surfaces; pain; behaviour of pain; treatments tried; length of treatments; what you do with your knees all the time etc. And is your knee pain due to feet-hip-other factors? There are other physios in the NHS.
Hope you get some help. Maybe be a little patient with physios, for some problems there is no quick fix. Just management.