This is currently allowed. In fact, most large health insurance companies do exactly that.
The GOP proposal, as I understand it, is to allow me, living in Missouri, to buy a policy from a company that is only licensed in, say, Arkansas. Said policy would only meet the regulatory guidelines of Arkansas, not Missouri.
Any reduction in costs this would generate would come from either (a) insurance companies flocking to the least-regulated states and offering these minimal policies nation-wide, (b) increased competition driving down premiums nation-wide, or (c) better risk-pooling by allowing insurers to have access to a broader market rather than just the state or handful of states their licensed in. Obviously different experts have different opinions on which of these would predominate and how large the savings (if any) might be.
Finally, the PPACA included something similar to this, allowing states to enter compacts that allow for insurance policies across their borders. Additionally, multi-state insurers will be allowed in underserved markets as long as they meet federal minimum coverage guidelines.