I think it gets to the fact that if enough people need to use private property, it is started to be considered as "common" and private property rights get eroded to the point that it can not be considered private anymore. Like "too big to fail", "too big to be controlled by anybody but the government" is a popular thing. Now, the nominal ownership may be or not be private, but with enough regulation the difference would be only in profit sharing arrangements and not in actual control over the property.

So when the parent post says "doomed to fail", it's not because there's something inherently faulty in private property. It's because people can't tolerate the perceived absence of control over such big things.