Push carts do carry a stigma in the SW, plus they are a threat to the important revenue streams of motorized carts. With the extreme weather in this part of the country, riding is the norm. The cost structure of the cart fleet and supporting infrastructure is highly fixed, and even if push carts only canabalize 10% of rounds, say 5,000 rounds a year, that's probably close to a $70,000 impact on the bottom line. Charging a trail fee for walkers would meet some resistance as Joe H noted.
Riders complain of slow play and a lack of "support" of the club's operations by walkers. Unfortunately, these charges have some validity. Unless walkers are willing to pony up via higher dues or trail fees and accept responsibility for fast play, a strong bias toward riding carts will continue to prevail. I don't like it, but the laws of physics and economics are not subject to change.