State corporations are private companies whose profit go to the government instead of an owner or investors. The place in North America that has the cheapest electricity is Quebec and that's because it's a State corporation producing it, it still makes billions in profit that is then reinvested by the government.

So no, free markets isn't necessary. Heck, the free market is what makes it so the US government is the one that spends the most per capita for healthcare even if it only covers part of the population.