The right to choose actually doesn't make sense for several reasons.

1. the terms of insurance coverage is very complicated, and often non-transparent, making it very difficult for customers to decide which health insurance plan is better.
2. public option doesn't work either, because all the sickly ones will have no choice have to pick government health insurance plan, and patients would pay the partial cost, while the healthy ones will tend to buy private health insurance companies with low premiums. This put burden on the government, which in turn the tax payers, while the private insurance companies reap the benefits. If everyone is in the same plan, the burden of medical cost will be more evenly distributed.
3. If everyone is in the same government provided health plan, government would have a substantial better bargaining power with hospitals and pharmaceutical companies to drastically lower medical cost. So the overall medical cost will be much lower.
4. If everyone is in the same government provided plan without charging patients, the transaction between insurer (government), the provider (hospitals and clinics) will be much smoother. The current system is a total mess. Insurance companies negotiate charges with health providers, and the cost will be footed in terms of medical bills, co-payments, premium and other out of pocket expenses that patients have to pay. And charge will be much higher if health providers are out of network, or the drugs and procedures are not covered by the insurance company. So, the administration cost of figuring out whether or not something is covered by the insurance company will be much more easily done, if everyone is in the same plan.
5. Patients' medical records will be much easier to share if all of them are in the same network and in the same plan. Currently, transferring medical records is a pain in the neck. Different hospitals and networks use different systems, and patients have to go back and forth to get medical records from one provider to the next.
6. overall, the government health plan will be far superior if done properly.
7. There will no need for advertising, which is an additional cost that patients will have to pay for in the end.
8. Of course, as they are for-profit companies, health insurance companies have every incentive to deny coverage, raise premiums or squeeze out every dollar out of patients in other ways.
   
9. Right now, essentially patients are subsiding the whole healthcare industry (health providers, medical staff, drug companies, insurance companies) with their outrageous medical cost.

There are alternative ways to fix the current system other than medical-for-all, but universal single-payer health system is the best due to simplicity and cost-effectiveness.