We have that now it's called Blue Shield. BS wants to not pay for my MRIs because they're "experimental>" Scripps calls bullpucky and provides stats and justification. BS still trying to decide if they will pay. So far they seemed to be saying that prevention is experimental, but if I get cancer they will pay for the treatment. Good deal.
Whether you're screwed by the government or a private for-profit company, it feels the same.
Until April 15th, that is.
Completely empathize w/your go 'round with the aptly-acronymed BS. My FIL is Military Retired Disabled and has to deal with the VA, so I understand the frustration.
Still, with the continued existence of private-sector insurance, at least there's a range of choices out there. You wouldn't get THAT with anything government run.
In my life I've been covered by Blue Cross, Blue Shield, Met Medical, and some other now-defunct company that was actually really decent, under both HMO and PPO type plans. With just about every plan I've had, sometimes things were a hassle. Met Mdical I don't think EVER got a single claim paid out correctly, nor on time; my wife had to bird-dog them on the phone about nearly everything. But, they did pay out eventually, and in full, so it ended well.
Never been cornered into taking a Kaiser plan; I think I'd opt for a plan run by ol' Jim Jones before I'd do that, but even they're a lot better than anything you'd get from an Uncle Sam plan.
Count your blessings; even if you only need one hand to do it.