There is no point in having a market, when only one option makes sense or it is irrelevant which option you choose. There is no point in having competition, when it cannot improve the product or any process of its making.
In these cases private ownership just leads to cartels or innovation in marketing departments alone, both rising prices.
Having said that, the difficult part is to determine these cases and to figure out how to transition the privately owned companies into public property without stealing it or overpaying for it.
Another difficulty is to judge, when something suddenly stops to be one of these cases (e.g. postal services with electronic messaging as an alternative to it).