Malcolm,
Great thread as a new poster. I am a major proponent of walking golf, and I walk and carry for the vast majority of my rounds. It is the best way to experience a golf course. Much of the golfing experience is lost when you are riding a cart along the sides of holes. There is something timeless about slinging a bag over your shoulder in the late afternoon. To me, it is the ultimate manifestation of golf as an individual sport. You have no outside aid; it's just you and your clubs.
That being said, caddie golf is very fun, and it has many of the benefits of walking and carrying with some added ones as well. Any club that supports both carrying and caddies is ideal in my book. At my club, Oak Hill, a member can carry (most of the low-handicappers do), take a cart, push a three-wheeler, or take a caddie, regardless of day or time. Though I wish fewer members took carts, it is an excellent situation.
As for your bigger question, I think most golfers simply don't have the time and energy to carry their own clubs. Furthermore, most folks who don't carry their own clubs have either never tried or do not have the right type of bag to do so. They do not know the benefits that are giving up by not walking and carrying. I think it is a US thing too: most English golfers either carry or push, and Scots either carry, push, or take caddies.