I'd rather have the choice of insurance company bureaucrats to deal with as opposed to government bureaucrats.
Agreed. And better yet, no third party would be involved. You would buy health care like you buy a TV set. You would walk through the door and pay cash. If you couldn't afford it you would take out a loan. If you had an expensive illness or accident your insurance would kick-in because it covered catastrophic events, not routine treatments.
You've hit on why we've had decades of employer-provided insurance in the first place: buying coverage in bulk used to be cheaper than each person buying individual unassociated accounts. Employer-provided health benefits remains the best way a person earns his/her coverage, while THE best and THE cheapest way would be single-payer.