The existence of private insurance is the greatest obstacle toward maximizing freedom of choice.
Freedom of choice, within health care at least, comes from fewer servicers. If you have 200 networks, hospitals/doctors won't deal with all of them.
A single payer system has just one network. All doctors accept it.
As it stands, employers choose what insurance you get. What insurance you get determines what doctor you can see. In other words, your doctor is more or less picked by the employer. You like my doctor, you lose the job that insurance is tied to, you lose the doctor you liked.
That's not choice. It's coercion to force you to stay in a job no matter how good or bad it is since if you get sick you'll be s.o.l. without that [likely dramatically worse than Medicare] insurance.