I'll admit I'm not familiar with healthcare in Europe, but surely there are people whose job it is to estimate the cost of providing healthcare and estimate the probability of certain health events occurring.

Yes, I am sure there are.

Worth noting, my girlfriend is a Neurologist. She and her colleagues say if you have anything serious wrong with you, go to the public healthcare system. You will probably have to wait longer, but you will get the treatment the doctors want you to have.

When the same doctors have to deal with private patients (many doctors have both private and public patients here) then its basically a battle with the insurance companies trying to justify why they should pay for the better drugs.

So you have doctors time being wasted on bureaucracy and form filling on one side (they would rather be treating patients), an insurance company person wasting time on the other side. Doctors time isn't cheap. I doubt actuaries are either. It seems blatantly obvious to me that the system without that aspect to it is way superior.

Sure you do. Your insurance premiums are your taxes. An actuary had to figure out how much revenue the state healthcare system has to bring in to be stable.

Well unlike insurance premiums, we don't get a choice in paying taxes. And the poor who don't have the money to pay taxes are still covered. So while what you say is true in one respect, its not really the same.

And it has been well documented that the American system is very inefficient compared to Europes.