That sounds really good, but there's the issue of networks of doctors and providers... The reason health insurance has always been localized is generally speaking, most people receive most of their care in a relatively small geographic area.
How, for example, would an Arizona based health insurance company, build a robust network in Rhode Island, and what's their incentive to do so given the already large Arizona population of insureds?
And insurance company can specialize in ensuring a certain "type" of people instead of just all types of people from one location.
For example if I wanted to specialize my insurance company to ensure only farmers and cattlemen, I would be able to capitalize on efficiencies and additionally be able to provide valuable information and risk management techniques because all of my customers are from the same industry.
The network problem exists in whole part due to the actions of government involvement in regulation in the health insurance market. Get them out.