I am being hypothetical with healthcare, and very idealistic. I admit it.
As for why people would get involved with cash only when they have insurance. Again, this goes back to my question about the type of insurance that is mandatory. If extremely low premium, high catastrophic is accepted, then lots of studies (I'm too lazy to find these right now

) show patients (relatively healthy) can save tons of money going down this path (it's like extreme health savings accounts). But if government requires only typical "feed the insurance beast" high monthly premium insurance, then yeah cash only could dwindle.
As for Dr. Noctor (which is a funny way of saying it), I just blame this on the stupidity of people. Again, I will only see a physician for my health care. I see my Fam Physician twice a year? I know what age he went to med school, where he went, where he did his residency, what his favorite clinical rotations were in school, what areas of medicine does he research and love to practice in his career, etc. Do people really not ask questions about their provider?
First, consumer protection laws exist precisely because consumers are allowed to assume things in our society, and if things aren't what they seem people are duped. When you buy a product, you are allowed to assume it will work for the purpose it is sold. You don't have to know if a knife is made of stainless steel vs tin to be allowed to assume that when you buy a knife it will function as a good quality knife. It's not really any different here. When someone comes into the room and introduces themselves as Doctor X, and is wearing a white coat, and says they are board certified in dermatology, you are allowed to assume that this is a physician who has completed a dermatology residency. It's not your job to say, where did you go to med school, where did you do your residency, what organization boarded you? It's great if you are that inquisitive, but it's not expected of you, nor is it required of you as a consumer. You are allowed to rely on the reasonable expectations one would have when a care-provider makes those statements. So yes, this is false advertising.
As for "free market" taking care of this issue, the problem is that free market works a lot better with goods than services. Laws like consumer protection, false advertising, etc exist because a non-expert can't always tell if they are being duped when the "product" being sold is someone's expertise. There have always been charlatan doctors in medicine, so called "snake oil salesmen" who sell useless products and customers rely on their expertise as physicians. There are even a couple of infomercials on late night TV that fit this description. That's illegal. But a free market doesn't correct for this because the consumer doesn't know any better, often until it's too late.
The real problem with letting the free market gauge the DNP, is that for, say, 80% of the office visits, the patient's complaint is not so significant, and someone with DNP training probably will handle the issue as well as a physician. What the physician really brings to the table is the ability to recognize and treat that other 20%. You think horses, not zebras, but you had better be able to quickly recognize those few zebras. So in theory a physician could go through a career never really needing a lot of their medical training, and an NP could go through a career never catching one of those 20%. And the free market would say, "hey, this NP provides equal service at a fraction of the price, this person is "better"). But that isn't true for that 20% who die because they didn't get physician care. This was the kind of argument that wasn't effectively made a few decades ago when physicians fought the chiropractic industry in court, calling them "quacks". I think most of us have come across a patient who ended up with a death sentence because they sought chiropractic care instead of physician care, and got manipulation when they really needed chemo. The same will hold true of the 20% who go to the NPs. You learn a lot in a longer schooling and residency. 1000 hours doesn't do what 15000 hours does in terms of preparing you for what you may have to deal with. It gives you a decent ability to handle the routine, which is what a lot of patients need, but it does a big disservice for the smaller group that actually don't have a routine problem. Now there may be a need to ration medical care, and to this extent an NP handling routine issues may be fine, much like a non-MD person working as a medic in wartime. But nobody should kid themselves that this is comparable care because even when they are doing the same tasks, the physician brings a heck of a lot more training to the table, able to recognize the not-so-routine things. But for the free market to factor this in, the public has to understand this, and they don't. They just see someone in a white coat who is introducing them as a doctor, accepting their insurance, and able to see them on shorter notice.
So NPs win in the free market -- shorter waits, cheaper, but provide significantly worse care on the X% of things their much shorter training neglects. Plain and simple. Do you want someone who can handle the routine but be lethal for the non-routine, or do you expect your "doctor" to be able to recognize when there's a problem. If the question is posed this way, most of the public will say they want their doctor to recognize problems. But nobody is phrasing the question this way, and, looking at the article, there is a lot of propoganda about how the NP is doing the exact same job as the doctor, and even calling their short derm bootcamp a "residency" as if it has anything to do with the grueling 3-5 years physicians go through.