Without getting too much into club finances, the club is able to succeed and grow due to the public/private model. I'm sure that they could charge more and still get plenty of play to support the model. The number of members is essentially fixed. It fluctuates slightly up or down.
Personally, I love getting paired with public play. I love seeing people play it for the first (or second, or third) time. Brings back memories of my first few rounds.