Are you saying you believe that there are no programs in existence, which are government-run, that are not "shit shows" ?
Of course, there are times when efficiency is not the thing we’re optimizing for. The Space Program is an example of a pretty great government program; there was no profit or benefit to private space travel in the 1950s and 60s so the government had to subsidize it, but now that we are starting to see private business catch up, the best thing to do is get government out of the way. This is not all that different during the Age of Discovery where kings and queens subsidized trans-oceanic travel.
IMHO government should only exist to fix free market deficiencies (Monopolies, unfair competition, fledgling industries, lack of players). Not to take over a market and try to dictate it from the top down. Ultimately the goal should be that all people make enough of a wage to afford healthcare and let the market handle it. And still have a safety net for those who fall through the cracks, but the safety net should never be the goal.