That's why I don't totally get why so many courses that are walkable won't allow it. It's not even cutting into their bottom line! Is it a misguided notion that walking is slower?
I think this is mainly it -- both from the management of the course and from other players. I've seen people at a public course get really upset when they are in a cart and are behind people who are walking. They are probably afraid it will drive away potential players.
I think this question is a pet peeve for all of us who like to walk; the presumption that walking is slower than riding really rubs us the wrong way.
And there's no doubt that on an uncrowded golf course, unless it's cart path only, a single rider can go faster than a single walker; in that regard, it's no different than anywhere else. Riding my bike is faster than walking, but driving my car is faster than riding my bike, but flying is faster than driving. And I can't walk as fast as a golf cart goes...
The irony of the conflict, though, is that when the course is crowded, say on a weekend morning, is when the course is most likely to REQUIRE you to ride, AND when it makes the least difference; if the round is slow and there's nowhere to go in terms of playing thru, it doesn't matter what your means of locomotion to your golf ball is. And that's when walkers get upset at being told that they are slower by the management.
At a former club of mine in Georgia (Crystal Falls) one of the most admirable things about the management was that they were just completely honest about all of this. During Daylight Savings Time, you paid half a cart fee as a "trail fee" on weekend mornings, and the club said flat out that it was a revenue issue and NOT a pace of play issue; lots of players who walked most of their rounds would go ahead and pay the difference and ride. During standard time, when the weather was much more likely to be iffy, no trail fee was charged; the club was happy to have you out there in the cold and wind and so forth. It was a thoughtful, insightful policy, and all of us who religiously walked our rounds really appreciated it.