You can see where this leads. Before long, the insurance "market" would be a single-payer show. The same dynamic would eventually push private players out of the employer-paid market as well, because the tax-subsidized plan will have the same advantage. Employers will choose it because it will cost them less.
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Socialized health coverage would leave them dependent on one monopoly insurer. If Medicare's continued slide toward insolvency is any guide, it would lead to out-of-control costs and big tax hikes down the road.