I am just back from an unplanned vacation in a hospital. In a very fundamental way, I know I was lucky. I live in Milan, in Lombardy (9.7 million people, GDP per capita € 33.500), where we enjoy good quality healthcare. In 1997, Lombardy established a quasi-market in healthcare. Although the Regional government finances the system, the functions of purchasing and providing care are formally separated, allowing for patients' free choice. As funding follows patients, private hospitals flourished and to a certain extent now compete now with government-run ones. Quality breeds reputation: Lombardy is consistently the Italian region that attracts more patients from the other ones.
The Lombardy system isn't perfect, but as compared with socialized medicine as we know it all over Italy and Europe, it is definitely better. It is the magic of competition: very often, just a little drop is enough to substantially increase quality and better check costs.
That healthcare needs to be more of a market and less a planned economy is straightforward and clear, when you witness from your hospital bed the wide variety of operations that go on all around you.
A hospital brings together factors of production that are very heterogeneous. People immediately think of high technology for diagnosis and surgery, and of highly skilled doctors. But just looking at doctors, it is quite amazing the variety of skills you do need to match to have a hospital that both works well and leaves patients happy, particularly when the hospital also offers learning opportunities to university students.
Think about nurses, who aren't all quite the same, as they differ widely for skills and such wide differences are mirrored in the different functions they perform. Plus, a hospital is up to a point a hotel, and a good part of your customer satisfaction is based upon only apparently trivial matters such as the quality and taste of food, and the courtesy and sense of humanity of the personnel.
If you are of a romantic bent, you might believe that people willing to do such a hard job (long hours and low wages) like a nurse's one should be driven by some kind of love-thy-neighbour principle more than by any other kind of incentive. There might be a hint of truth in this view, but in our prosaic world it is much better to work to set and maintain a standard in conduct - as McDonald's or Starbucks do, with their personnel.
Such a variety of factors of production requires strong management skills, of the sort that bureaucracies seem rather unable to foster and attract. Even if you believe that government should be involved in financing access to care for everybody, you'd better recognize that managing a hospital is a horribly difficult job - of the kind that calls for the ingenuity of private enterprise.