My club has always encouraged walking. I'd estimate that about 15% of our rounds are walkers who carry their bags, 35% are riders and 50% use push carts (trolleys). My experience is that unless there is only one rider in a cart, the walkers almost always play a faster round. Typically, when there are two players in a cart they drive to the first player's ball and the second player sits in the cart and doesn't go to his ball until after the first guy hits, cleans his club puts it back in his bag, fixes his divot and gets back in the cart and then drives to the second guy's ball. By then each walker has already gone to his ball and hit (or is ready to go.) Walkers at our club usually play ready golf simply going straight to their ball and hitting it. Riders don't because they want their bag with them rather than taking a bunch of clubs off the cart and carrying them ahead to their ball. Also, riding carts are not allowed within 30 yards of a green so the riders spend time walking back and forth to their carts while the walkers just go the straight route. When we play a four ball with two walkers and two riders, inevitably the walkers are waiting for the second guy in the cart to hit and the riders rarely wait for a walker. I note that our teeing grounds are close to the preceding greens except for one hole. Riding would be faster on courss where the tees are distant from the preceding greens.
This morning we were the second group out. The first group was a twosome: the club champ and another scratch golfer. Two of their regular playing partners didn't play because of the bad weather. They usually walk, but rode today I assume because of the rain. Their foursome often plays just ahead of us and both groups play between 3 Hrs 40 min and 3 hrs 55 min. The club strongly encourages all rounds to be sub 4 hrs. When any of us play as a twosome and get out first in the morning we play in less than 3 hours walking. Today my foursome played in 3' 40" . The riding twosome played in 2' 55"... no faster than they would have played had they walked. We took approx 355 strokes collectively. The twosome I'm sure took less than 155 strokes. I know this is not scientific, but my experinece tells me that in most cases, at least at our club, 4 walkers are not slower than 4 riders.