In the current US I don't believe it would. We have significant numbers of people going to naturopaths, chiropractors, and many other BS practitioners in spite of the mountains of evidence that what they practice is almost completely BS. The major thing that nurses get that many physicians don't is the customer service aspect of medicine. I've seen numerous NPs joke about every patient getting a door prize (usually in the form of antibiotics or steroids) when there is literally no indication for them at all because it makes the patients happy. Patients care a lot less about their negative outcome when they feel like they were treated, even when that treatment was BS and those are the patients who seem to advocate to going to an NP over a physician.
I'd like better data as well, but my experience comes from more than just my time as a med student. I worked in various healthcare settings before med school and the two fields that always seemed to think they knew more than they really did were nurses (the more experience/education, the worse they were) and Paramedics who thought they knew more than the ED physicians. Most of the people I worked with were fine, but when I saw real issues it was almost always with advanced nurses or those wanting to pursue that path.
What makes you think there's so many more DOs from new schools matching into TRI's than MDs from new schools? Why do you think standards aren't being kept high (COCA standards are becoming stricter with time) or that they're dropping? And again, do you really think DOs would still be doubling if there were already as many grads as MDs? It's easy to double when your baseline is 1. It's a lot harder when the baseline is 100. How is this even being argued? Also, DOs have ACGME match rates in the 80's, overall match rates are much higher (comparable to MDs). We'll have to see how that's affected with the merger, but the number of residency slots isn't dropping, it's increasing, so why do you think overall match rates for DOs is suddenly going to plummet?
Just so we're clear, I have a big problem with the expansion of schools accredited by COCA, but I also have a big problem with the expansion of schools accredited by LCME as well. We don't need any med school expansion unless we're going to significantly decrease the number of IMG and FMGs allowed to enter the match. I would personally love for COCA and the DO degree to be absorbed into the LCME and MD degree as it would completely standardize physician education, but I think that's just wishful thinking on my part at this point.