In theory, no. A private company (by the commonly understood definition) always needs growth and profit to continue providing a good service. Neither of those things are compatible with being cheaper than a provider that doesn't have to optimise for those things.

Obviously in practice that's not how things work out, so in most cases private companies end up moving faster, leveraging efficiencies, utilising innovation better, and generally being cheaper. The lesson shouldn't be that means the government shouldn't provide services though, but rather that the government should act more like a business and do things businesses do to be competitive.

It's very noticeable that when government does this it works really well. The UK government has brought a lot of it's web and IT services in-house in the past decade, and they're so much better now.

I never said all services should be socialized. For example, I don't think auto repair services should be socialized. Do you see how silly your statement is?

And no... there is no way that a private company could offer something cheaper because both entities function the same way except that a private company also has to make a profit. Governments are not profit-making entities. Take whatever method a private company has to make something cheaper and remove profit and you have something the government can handle.

I didn't realize we were talking fantasy hypotheticals. Reality is, private companies can and will always do better than the government in almost everything. For the exact reason that you claim to be the problem. They want profit.

Industries like healthcare are plagued with government interference. Some regulations are important. Many just serve as a moat around the oligopoly that is the current private health Care system.

No one's talking fantasy hypotheticals except for you. The "reality" that you're claiming is not at all actually reality considering that every other industrialized nation on the planet pays less for healthcare and prescription drugs than we do in the United States. If private industry can drive prices down, then so can government. The USPS was the poster child for efficient and effective government service until Republicans decided to absolutely decimate it because of lobbying from private industry. Government services don't need to make a profit, they don't need to lobby, and they don't have any of the greed-driven motivation that private companies do.

You're either being intentionally obtuse or you're intentionally being misleading for some reason. This isn't rocket science. If two things are equal and one has the requirement to also generate profit, there's no way the other can possibly cost more.