The private part is still important. It's a legitimate fleet of military aircraft that would rival the air forces of many small countries that is directed by a man who really isn't accountable to us outside our borders.
This isn't new territory, it's just that you have to go back a few hundred years to see small groups of private individuals accumulate this much physical force. Just think about some of the disagreements that have occurred over scare resources for responding to the pandemic. Imagine how that picture can change.