Anyway, I'm guessing the answer to your question is: control. You know that you can at any moment tilt your head forward and lose the vertigo sensation. So you are safe and in control and you also feel safe and in control. That makes the experience enjoyable (I assume).
OTOH I love stepping down an escalator 2-by-2, the brain has to calculate how far the foot should jump given the size of the steps and the pace of the landscape, it's fun.
It might also allow you to start a short conversation with the traveler above you, eg. "I have vertigo which makes going down escalators tough"... would that sort of distraction be helpful or not?
Exceptions: poetry, music, jokes and other cultural expressions.
Before then I was always chasing my own tail with 'what do they mean?', which is pointless, if they meant something they could say that particular thing outright and get it over with.
This is symmetrical, so, I don't want to 'wash my hands', I would like to use the toilet. When I'm hungry I say so and when I say 'no problem' it really means that so we can move on.
All in all this made life a lot easier, though from time to time it can make for comedy.
As I say, I try to avoid the escalator, if nothing other than to be courteous. However, sometimes I use it out of courtesy as well, such as when I'm with a group of friends, and don't want them to have to wait on me. When I do need to use it, I've developed a pretty good system of keeping the anxiety in check - sort of a deer in the headlights approach, where my gaze is focused on my shoes.
Visual inspection of https://www.youtube.com/watch?v=7fNDgwp_w_s suggests that when two people enter the escalator side by side, the walker exits the escalator at about the same time as the stander is 75% of the way up it (~=133% of the rate of speed). The density of the walking side is surprisingly high to me (maybe accounted for by the short span relative to the monsters I'm used to on WMATA MetroRail), about 60% of the standing side. This leaves 80% throughput for the walking side of short-span split escalators relative to the standing side, only a ten percent overall cut in capacity for this one escalator in Singapore.
That number will probably go down the taller the escalator is, as the walking side slows down due to personal stamina (adjusted walking speed and percent willing to walk), and bunching, a phenomena we're familiar with from busses.
That assumes that everyone is capable of walking on an escalator. I, for one, am not. I get vertigo, and am on the brink of a panic attack for the entire duration of my ride. I can barely step on one, let alone walk, particularly when going down.
I do look for an elevator whenever possible, but there are times when one is not available and I have to work myself up to the task. I have to grip the handrail with both hands, and focus on a point on the steps themselves.
I'm sure there other issues that people have - like being able to walk but not climb - that would prevent them from being able to walk. Therefore, it's best to have the option to stand on one side and walk on the other.