In regard to the non-academic aspects of private school, that makes a lot of sense. I never actually realised that people would pay extra money for crazy amounts of house events, religious education, sport at inconvenient times of the day, and the opportunity to spend even more money on frivolous events. My cynicism aside, I can see why you might want to choose that sort of thing. Aside from being quite holistic, and I'm sure, at times, even enjoyable, it seems like it has a nice aesthetic as well, as though you're on the set of Dead Poet's Society, or something.
Personally, the thought of early-morning rowing sessions, school chapel, showing unrelenting enthusiasm and pride in an abstract institution, as well as 'survival' camps doesn't appeal to me in the slightest, and I believe these things are quite unrelated in the formation of an identity. However, I totally respect that others probable have a different outlook than me.