I relate very closely, having had the same thoughts over the past few years. Social clubs sound good in theory, but in my experience it's difficult to connect with people without a central activity or subject to act as a touchstone. It's a frustrating sort of paradox where the best social groups diverge greatly from their core theme, and yet the core theme is necessary to reach and maintain critical mass.
I think it's possible to get around the problem, but it would take just the right structure; there should be activities, but enough of a variety to have something for people from all walks of life. But also not too much of a variety so as not to appeal only to those interested in constantly trying new things. Perhaps a set of some baseline, fairly universal activities, with space for individual members to share their own hobbies and interests from time to time in a group setting? I don't know exactly, but it's something I've been considering for a while, and it feels like there must be an answer somewhere in there.
> I think it's possible to get around the problem
Could you articulate what you perceive to be a problem with all that?