Not a fact. Easily demonstrated by falsification by examples of each of those where they have failed because of centralization. Infrastructure is deviously hard to get right. Edit: we can find examples of decentralized infrastructure that works great (internet, Apps, banking).
Healthcare in particular must always fail because there's an unreasonably infinite cost for and ideal service. There's no good answer to what price (what resource limitations) we should put on fixing little Jimmy's cancer. Governments struggle to make compromises in healthcare, and plenty of citizens are super unhappy with any compromises made. Of course a free market can't fix that problem either. Disclosure: I'm not a free market zealot.
Too many people want to define sides and then get idealist about "their side"; how tiresome. Perhaps you are similar to the free market zealots?
> I believe housing too could be on the
Be careful of what you wish for. Government housing is rarely brought out as an example of success? Maybe Singapore. "Too much government" is a common reason for housing (market) failure. Supply availability is mostly constrained by regulations. Demand is driven by desirability. House prices are driven by mortgage availability in developed countries. House unavailablity is often because of governmental choices over regulations and interest rates. Governments obviously mostly fail to get those right. What makes you believe a government can get socialised housing right?
We don't have infinite resources. Neither government provided services nor free markets solve that. Anyone answering with either of those solutions is the same.
You might find this article interesting: https://washingtonmonthly.com/2020/08/30/libertarians-took-c...