I had a long conversation with my buddy on this topic last year when we were touring England and discussing the UK model vs. the US.
Both of us are Gen X. He's mid-50's, I'm mid-40's. He has no kids, I have one. We both do pretty well career wise, are quite modest in our housing and don't expect to move soon, so can certainly afford golf as a luxury. We would be the ideal demographic for a private club.
I live in south Orange County, CA and he lives in Nashville, TN. In both locations, the high end public golf offerings surpass the private golf offerings. There is nothing architectural of note in either location, neither of us care about a pool or tennis courts or a fancy clubhouse, so why would we spend $50-100k on initiation and $10k a year of our golf budget on one decent but unremarkable golf course vs. a 'club card' at a high end public course(s)- leaving thousands a year to spend on travel for golf?
Even if could get over the initiation and was happy playing the same course twice a week every week, 100 times in a year, the value proposition still falls short. The golf courses are simply not good enough to justify the expense. Unless there's a price correction (unlikely) that won't change.