It is a bit simplified but it is much more streamlined than the insurance system outlined.

The UK model is single payer. The government pays the money into a national body like NHS England (or NHS Scotland etc) and it distributes money. The internals of the system itself are complicated (there are commissioning groups, acute hospitals, mental health services, dental services, public health services etc) and have overhead as with any organisation.

But there are not multiple government health organisations or paying systems - there is a single national tarrif for what each part of gealthcare costs and that money is distributed down to the providers like hospitals and GPs/family doctors. 2/3 of the cost of Healthcare is staff wages; it's people intense.

No insurers, no billing agencies or debt collectors. Essentially there are not 3rd party businesses creaming off money for doing little more than handle the money. More of the money goes directly to healthcare rather than intermediaries. The infrastructure and administration within the system such as commissioning groups etc have fixed costs - none of it is run for profit.

In terms of government control - that is a concern but US politicians already heavily interfere in the system. Abortion is a good example of that. What you don't get is Healthcare businesses of various types interfering in government.

The real issue for a single provider system is the staff - wages are kept down as its a national system. That causes strife if wages of pushed down too much. So you do get unions exerting pressure on government. I see that as a good thing but your mileage may vary.

Also if there is under investment then that can severely hamper the system - we have that problem in the UK - demand is going up as the population ages, but the politicians won't make the hard choices of taxing the elderly to support expanding the Healthcare system.

I would earn far more in my specialty in the US. However even so I much prefer the UK system. I don't want us to go down the route of the very broken US system. However there are public system with insurance models that do seem to work well - Australia and Canada have good reputations both in terms of cost, efficiency and pay for staff etc.

Essentially Universal Healthcare should be the aim, and it doesn't necessarily have to be a single payer system to work. But single payer systems can work.