I'm no fan of our current healthcare system, but your description of dealing with private insurance is very much at odds with my experience. It has always been very simple and easy for me. (Doctors are a another story)
I never had a problem either until you try to anything outside of the ordinary. My wife needed some special treatment it was a nightmare to get approved I wasted hours on the phone to be told that the procedure was through another insurance company my company hired for this special procedure. They made so many mistakes I had to call once a week. At one point I had a 4 way conference call between both companies and a special hr person from my company to get this shit sorted out.
That is what pushed me to socialized healthcare private insurers can get fucked.
There are a lot of factors that determine how hard private insurers are to deal with—the kind of plan you have, the type and intensity of care you need, and the quality of the providers in your area/network—so experiences will vary significantly. I am genuinely glad it has not been so bad for you, and I’d love to say my experience with private insurers is the outlier, but unfortunately I suspect it is the other way around.
Every US-based friend or family member of mine has at least one horror story about a surprise bill, a Kafkaesque nightmare of denials and prior auths, being unable to afford their medications or doctor visits, unrealistically low annual visit limits (Depressed? No more than 12 visits per year to a therapist should cure that!), “copay accumulators”, and on and on. The podcast An Arm And A Leg[0] offers a disturbingly wide variety of stories of this bullshit and all the things you have to learn just to protect yourself from getting completely screwed in America’s privatised health care system.
It’s endless, and it’s exhausting, and it’s even more exhausting when folks like the OP show up to make baseless claims that government-run care is somehow going to be like going to the DMV because they’ve swallowed this “government is the problem” bullshit. I’m not going to sit here and say governments are infallible, or that Medicare is perfect, because they aren’t and it isn’t. But do you know which insurance plans in the US have the highest patient satisfaction ratings? The government-run ones[1]!