Of course they aren’t interested—the default model is working for them right now.
Take away the default model, and open pure competition, and the insurance companies will have to compete on that level, and things will relatively quickly get better.
The providers still hold the key to pricing. When your choice of hospitals or specialists is limited, you’re going to go with whatever insurance company they accept, or pay some exorbitant price.
The problem is that most people don't pre-shop for insurance that way, and only find out that their local provider is out of network when it's urgent that they get help.
Even if you plan it all out ahead of time, you end up in emergency surgery in an in-network hospital, with an in-network surgeon, only to find out the anesthesiologist was out-of-network. And you still owe tens of thousands of dollars out of pocket. It's a bad system all around.
Insurance only gets cheaper the larger the company gets, because the risk pool can absorb more risk. Competition doesn't improve it.
A giant problem with getting healthcare through insurance companies is that it's not actually insurance. Insurance should only be used to pay out in catastrophic cases; it's always cheaper to pay for something predictable yourself than to make an insurance claim.
Of course, most people can't afford any healthcare at all. There's no way to insure that.
Don’t seem to have the problem in the UK. Everyone has healthcare. Those that can afford to (or their companies) top up with swanky perks, but it’s not needed for most.
Total cost is $2800 per person per year.
In the US it would cost $950b to provide that for everyone.
The US currently spends $1077b on Medicare/Medicaid.
Take away the default model, and open pure competition, and the insurance companies will have to compete on that level, and things will relatively quickly get better.