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accept the best plan

Why not have a single-payer plan and private plans from any insurer who wants to participate. You still have the 10 essentials to make the quality consistent, and bronze, silver, gold, and platinum levels of copays and deductibles. No reason why a single-payer couldn't offer those four levels too.

Then let consumers decide which one they want. The single payer would be 15% cheaper just because of the overhead, but some people might decide they want XYZ brand and pay more. (I predict that no insurance company would choose to compete after the first year.)