Finance management major here, I'd argue that governments aren't inherently inefficient.
On a local level, government organisations are essentially the same as non-profits. The only difference is in who they are accountable to. Even KPI are pretty much the same.
The inefficiency of a government in contrast to the free market is in its inability to adjust to people's needs quickly on a global scale. Imagine a company that has to sell a little bit of everything and then some. What kind of resource does it need to have to fully satisfy the demand? It's practically impossible to make a vertically integrated system that would do this amount of research, let alone organize all the production and supply chains. It doesn't matter if it's a government or an entity. They all will drown in beurocracy, except the government is usually stricter as they tend to play it safe.
Hence, it's really a non-issue if a government takes control over parts of the market. And because they can't facilitate it all, they take over socially significant parts of it, like municipality governance, military, and healthcare.
Also, you (the person reading, not the person I'm responding to) should never be mistaken in thinking that the free market is perfectly efficient. It isn't. Creating points of inefficiency drives a lot of revenue. Think purposefully limiting demand to drive prices up. This is what's happening with insulin in the US, for example. If you have perfectly inelastic demands, you can make your product infinitely expensive.