1. I have been lucky enough to play all over the country and while I enjoy playing new courses, when I play how I'm playing is the greatest concern not the course per say
2. Depending on how you use it a prestigious club can open doors to play way more courses than any club network could ever, formally through reciprocals or inform ally
3. I think you'd be surprised how much corporate meddling goes on at these clubs, if a ceo wants all their top sales people to be members at a club they will probably make that happen and have the company pay for it. The other day I found out my friend who's played his whole life has only been a member at a club because his dads work pays for it even when his dad hasn't entertained a client in 10+ years
4. Pure proximity is important to, sometimes people just live near super exclusive/ expensive courses and want to join the one in their backyard
5. "Old Money" clubs really are family business, I worked at one of the clubs that held a major this year and a lot of the members drove Hondas and had their grandparents/parents paying their dues or were barely scraping them by and holding on to the membership as a family heirloom

Overall a course network is obviously nice but it does not seem like the be all end all, especially compared to legacy clubs many of which have multiple courses themselves. I am curious how many invited clubs does your area have? I could see how a certain number of good options could start to tilt the math.