In my mind, the degree letters themselves aren't particularly important in this regard (think DO vs. MD or DDS vs. DMD). What's more important is the professional title (i.e., "psychologist"), which we've at least legally protected in most/all states.
Yes, the Psy.D. was initially envisioned as a way of producing a professional degree akin to the M.D. or J.D., and to address the fact that some Ph.D. folks studying clinical psychology were getting little to no actual clinical experience (which, I believe, is also why the mandatory clinically-focused internship was adopted). However, I would make the argument that particularly at the time of the Psy.D.'s inception, psychology as a discipline wasn't nearly as mature as medicine, and thus wasn't (and perhaps still isn't) ready for a fully professional degree. Beyond (and related to) that, our conceptualizations of mental illness are continually in flux, even to the extent of attempting to define what the "normal" human mental/emotional state entails, which largely is not the case with medicine and physiology where absence of disease is (generally) more readily-identifiable. Thus, to universally adopt a practice-oriented degree is to then distance ourselves from research; however, I feel it's our significant training in, and understanding of research that is one of our greatest strengths.
And as JS mentioned, given the average salary of psychologists, I feel that the fully- or at least mostly-funded modality is the most appropriate model, particularly as there isn't evidence it wasn't capable of meeting supply-side psychological needs.
Edit: Although yes, to address the last part of your point, physician lobbies and professional groups are much, much more effective than ours. Probably because they give them lots more money. Then again, ask many physicians and they'd probably tell you that nursing lobbies and organizations blow theirs out of the water.
