I still carry a high end insurance plan because if I break my leg on the ski slopes I don’t want to end up being triaged into the “indigent” bucket at the ER (this happened to me once, luckily with something less serious than a broken leg). Likewise it’s hard to get into some specialists unless you are in network. This isn’t a case when a call from my primary can’t get me an appointment (that call has gotten me seen even by docs who are “not accepting new patients”) but because the hospital administration doesn’t like cash payers even though they are charged the most.
The real differences lie elsewhere. For example my primary doctor simply doesn’t accept insurance of any sort. I see her, I pay the bill as I leave. She chooses tests and therapies based on whether she thinks they are worth it (risk vs informative value), and has the time to discuss with me. The longest I’ve had to wait for an appointment was once when I called in the morning and couldn’t be seen until the afternoon. She seems to be friends with the heads of various departments of a few local hospitals which cuts through red tape.
The wealthy 1%ers and 0.1%ers have special areas of high end hospitals and various sherpas who can make sure the patient gets the attention they want. I wonder how that system is operating these days in light of what COVID has done to the hospital infrastructure.
Apart from my primary care physician, I’ve had better care from more egalitarian systems in Europe and Australia. Even there though, the informal networks are quite valuable.