Free healthcare is delivered efficiently, free at the point of use, in many countries. This is an established fact. Now consider a communist society. In this system, the employees in the state healthcare industry are not paid. They receive no money at all. However, the state has taken over completely free provision, not only of healthcare, but of housing, food, water, and everything else the healthcare workers need. Therefore they don't need to be paid money to maintain a happy and healthy life.
You may wonder how the state gets money, then, to build hospitals and schools, if everything is provided free, and there are no private industries or wages which tax revenue can be collected from. If the state takes in no money, it seems certain that they will be unable to pay for any new construction projects. But the fact is this: not only does the state face no wage costs, but they face no construction costs. Construction is really a wage cost paid to construction workers, and indirectly to the people who dig up the stone and other raw materials. These workers also don't receive a wage in a communist system, so construction becomes in this sense 'free'.
Now you may wonder, if the state is not paying doctors and nurses, or controlling the construction of schools and hospitals, what is the use of the state in this system? Why bother employing the stiff, tie-wearing tyrants at all? In fact, you are correct. The state being an unnecessary evil, it has been abolished.
But, you may wonder, without the state who will plan the economy? How will the construction workers and the doctors and teachers know what to do with themselves to create the orderly deployment of labour resources in different parts of society which we see every day?
The truth is this. Not only politicians, but everybody really wants an orderly deployment of resources in society. But communists don't think someone with a megaphone is the best person to do it.