The proposal to have video or audio recordings has come up a number of times, and there has been an objection with respect to privacy.
Of course, physicians retain patient medical records on all sorts of very private matters; it's just that they're in written form instead of in recorded form.
It's not obvious to me how having a recording in the file as opposed to having a written note in the file raises any additional privacy considerations, provided you're not uploading it somewhere, of course. In fact, the movement toward e-health records particularly underlines the fact that there's no substantive difference between an audio or video file and a written file, from a privacy perspective.