Do you understand what the "Captain practices" are ? Happens every year and yes coaches know about it and encourage it. BUT it is open to anyone that wants to attend that is on or trying out for the Varsity. It is a way for the players to get workouts in before practice officially starts. What you may or may not understand is they don't start practice like Public schools months before the season officially starts or hidden in gyms and when practice does start the have cuts to make so getting ready is a little tougher than most if not all. They don't have a full indoor field to practice on all winter. So getting the kids to organize and run the practices is a good thing and necessary to get ready for the season. If you ask any of the boys they all know about the practices but may be a little intimidated to attend because it is run by the players and tends to be a little tougher on the arms.
Most schools, public and private, with a decent program have such "captain practices" or "open gym practices". It is the place to weed out the weakies. And is done with most sports.