I'm pretty sure I would never join a walking-only club.
The ideal for me would be:
-Walking permitted at ALL times
-Caddies available, not mandatory, and available at a reasonable cost. I do not need some guy giving me fist taps and stroking my ego like some of the Bandon caddies do...everyone knows the type. I'd rather pay $40 for a guy that shuts up, carries my bag, tends the flagstick, and cleans my ball, than pay $80 for a guy who tries to make me feel like a tour pro.
- Carts available (sometimes I just don't feel like walking...if its hot, if its going to rain, if I need to play in 2 hours)
The most annoying thing to me is "Cart Path Only" whilst also prohibiting walking. My course has a no walking before Noon policy on weekends, and that remains enforced even if it's cart path only. I do not know of any official study done, but I believe walking is faster than cart path only carting in many cases, or at least equivalent.