Once in a while rain will require cart parts only, or work on courses. I find that riding a cart when it is cart paths only is worse than walking, except for the bag of course and the light weight bags of today make that not so bad, if you empty your bag and only leave a couple of gloves and a few sleeves in there.
At Kiawah, the Ocean Course you can't walk until the afternoons. They have caddies much like BethPage does. WInged Foot has two 18 hole courses and no carts are allowed except for handicapped players and they are required to have a caddy, no place to put a bag on that cart. Shinnecock Hills was caddy only when I was there as well. In Scotland we played lots of courses, and only 2 of them had carts, we used caddies instead.
We did use the electric carts, basically a pull cart with a battery at a course in Scotland that I can't recall the name of, Scottish Open was played there recently. I actually liked those once I learned how to use them, they would not be good for hilly courses but for fairly flat courses they work great, my friends say they will laugh at me should I buy one though.