State Farm Texas competing with State Farm Kansas is surely going to solve all our problems.
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.
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.
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.