Of course, if all (or most) private insurors were to do that, we would then have to rely on the Fed to provide such coverage? A back door to single-payer? Some speculate that this was the ultimate plan all along.
If private insuors remain in the market, but their pricing structure is too expensive, that would also be a route toward eliminating the private sector as people sought a "government option" (the state exchanges? or another route to single-payer?).