Considering I don't see many private ownership of the means of production these days. Indeed, do not forget the amount of nationalisation in the west, nor forget that combines and corporations however defined are by definition corporate and thus public entities. Not that these entities are benign and benevolent by nature but that's beside's the point.
Capitalism is frankly an out dated classification. As is much of marx's pseduoscientific gibberish.
Then again wouldn't want to rob people of their narrative.