While I agree you are either a slow player or fast player, I disagree with the first quote. What happens that makes carts slow is when Player A sits and waits while Player B hits their shot, then they drive over to Player A's ball and Player B sits and waits. If they were both walking directly to their balls, at least they wouldn't be wasting time like that. Or, Player A is done with the hole and in the cart ready to go to the next tee, but has to wait for Player B to get in the cart too (after probably collecting his wedge from the other side of the green). If they were both walking, at least Player A could be at the next tee and ready to go while Player B is catching up.
I understand that when used properly carts are faster than walking. I just rarely see them used properly.
Trouble is, I've watched far too many walkers do the same exact thing, only they don't move as fast as a cart. As was astutely pointed out above, slow players will be slow no matter how they get around. You can't make any sort of judgement on this unless you've done as I have and worked as a starter at a busy facility for several years and seen more than just the group in front of you. Part of my job is to track pace of play at the turn and the finish, and I can guarantee that the generalizations I see on both sides of the fence every time this topic comes up are mostly due to insufficient observation or to personal bias.
Slow players play slowly. It's as simple as that. They don't use carts properly if they ride, and they if they walk, they stroll down the middle of the fairway in a group as if they were window shopping at the mall. I've had equal numbers of pace of play issues on the job with both riders and walkers. When I was a walker (and I was for 25 years), I was a fast player. Now that I'm a rider, I'm even faster when the course is open in front of me because I can simply travel faster in a cart than I can walking, and the rest of my game routine hasn't changed.
I have a couple of friends who I play with often on weekday mornings. Two of us ride and the third one walks. The walker is not a slow player, but he has to work to keep up with the 2 of us in the cart. It isn't unusual for both of us to play our 2nd shots and still have to wait for him to get to his ball. It's a simple fact that when we are traveling at 10-15 mph, we are going to be more efficient when on the move than he is walking at 3-4 mph.
And by the way, none of us has any issues with the way the others choose to get around the course. We are friends enjoying the game together and that's all that matters to us.