I've never claimed I thought totally private healthcare might be 1/3 the cost of universal healthcare. I postulated the functions of our government as currently implemented might be able to achieve for 1/3 the cost if privatized. You invented some straw-man that argued I was arguing vs something else, something our government isn't even offering, so I'm unsure how you even got to the point you got to.
If you truly thought our health care was privatized it's all a moot point, because it wouldn't have been included in our original argument. In either case your point is moot because I never compared to hypothetical socialized healthcare but rather our current entire government system.
It blows my mind you would even use the "1/3" statement if you thought it was private because if it was private it wouldn't have even been in the subset of stuff I was comparing relative cost to. I never claimed private things would cost 1/3 the price of things already "private."
Paying for the inefficiencies of private healthcare is about half of US govt spend on providing services (the only larger spend is transfer payments, and you can't pay $4b in annuities to senior citizens from a private insurance scheme that takes in significantly less than that. So probably you need to cut healthcare by more than a third...). I actually believe the US could stay safe on a much lower military budget (though god knows what a private donor funded military would look like) but that's not getting the overall budget cut by a third even if you zero it out.
Mathematically impossible to achieve the functions of the US government for a third of the cost without cutting healthcare spend. Which has been demonstrated to be entirely possible by other countries, but only by choosing to let more people die or, ironically, removing some of the dependence on inefficient private companies for provision...