Looking at education and public housing, government run health care is nothing I want to see. Neither does Arnold Kling, and with good reason.
The main proponents of "universal coverage" want to throw more money at the current health care system, which strikes me as unwise. I believe that the "universal coverage" mantra is dysfunctional for the same reason that "more money for public schools" is a dysfunctional mantra for education. When your current approach is digging you into a hole, the sensible thing to do is not to dig faster. It is to stop digging.
I'm not sure what the answer is to ensure that everyone needing medical care will get it, but I do know that socialized medicine is not the way to achieve it.