Due to licensing and a doctor's ability to exempt people from criminal prosecution based on the exercise of discretionary judgment via prescriptions, I would deem them state actors and find the delegation of judicial authority unconstitutional.

I note that I can't get most labs without a doctor's order, i.e. I cannot make determinations about my own health without using one.

Imagine if you could only access law through lawyers, and they only let you read what they believed was necessary, and they had to approve every legal act you did, including entering into contacts, and the government forced you to have legal insurance to cover the costs for the "public good."

Doctors have what I consider a very bizarre power over the people, and one we wouldn't condone in other contexts. Most people just don't see it because "its always been that way" during their lives.