Also, it doesn't necessarily give you a chance to test out your training improvements. For me, my private league match occured and hour before training happened so the players don't play with the improvements for that week. Private league is a bit of fun and competition playing different people with no harm to your team. PL is more fun if you know the people in your league as well so there is a bit of rivalry.
One thing PL is good for is to try out different tactics and lineups.