Currently, health insurance is regulated by State insurance commissioners. If you have a problem with your insurance company, at least in Wisconsin, you can file a complaint. Now, let's imagine you have purchased insurance from an insurance company in the State of Alabama. If you have a problem with the company, say they refuse to pay a large hospital bill you think is covered under your policy, what do you do? Under the Republican proposal, I'm not sure. You can't appeal to the State of Wisconsin, since they don't regulate Alabama companies. You probably can try to appeal to the State of Alabama and file a complaint, but on their website they say "Our mission is to serve the people of Alabama..." and you are a Wisconsin resident. Good luck with that appeal.
Or, possibly the Republican Party had in mind a Federal Regulator who would regulate interstate commerce in health insurance. Somehow, I don't think this was their intent. My guess is that their intent was to leave interstate commerce in health insurance unregulated. Since Republicans believe in the free market, let's imagine what will happen. The first avalanche of rejected claims and resulting health care related personal bankruptcies, will force people back into buying insurance within their own state where they have legal protection. This is common-sense?