Standard spoiler warnings here. This information covers Episode 8 of Season 2 of Attack on Titan.
Towards the end of Episode 8 in Season 2 of Attack on Titan, we do see Commander Erwin travel across the wall. Shortly after, you see that they have a rather simple lift system to transport them from the ground to the top of the wall and vice versa. From the series of shots that feature the lift system, only 1-2 horses can ride the lift at a time. But they do appear to have more than one lift as three separate lifts can be seen from one particular shot in the episode. That being said, the lift system looked incredibly inefficient and slow.
Also, more spoilers below from the anime and manga, but the formatting prevented me from listing and hiding the content so please read at your own risk.
So, using the information from Episode 8, and from other places within the anime and manga, let's do a recap of the relevant information:
- The walls are circular and never connect to each other in any way, shape, or form. Using the photo attached for visual comparison, you can see that none of the walls connect to each other. Ground transportation usually occurs at doors, or entrances, found at certain points along each wall. If you were to look at this mathematically, consider Wall Maria our very own geometric circle that has two circles inside of it (Wall Rose, Wall Sina). And, being a circle that encloses two other circles, we can agree that the center of Wall Maria will also be the center of Wall Rose and Sina. Therefore, the fastest way to travel within Wall Maria, Wall Rose, and Wall Sina, will be along the radius of the circle (through the entrances of the walls, in this case) and not the circumference (along the wall). I think we can agree there would be some exceptions to this, but for the most part, you would want to travel through the radius of the circle, usually in the direction of a wall entrance, as that would be the fastest way to your destination.
- The current lift system, or what little of it that we saw, is incredibly slow and inefficient. The lift system could transfer only 1-2 horses at a time. Because of the inefficiency, the time taken to transport horses via lift would lead to time added to your journey. You would need independent operators, aside from anyone in the squad, to operate the lifts when you want to get to the top or bottom. You would need lifts on either side of the wall, and to make this most convenient you would need them in several locations along the wall. Since you need operators for the lift, the lifts would have to be located near populated areas, and the distance from a lift to very rural area along the wall may limit your operators which may limit your lifts.
I know it seems safer to travel the walls to get to places, but in most cases our heroes are rushing to a location for damage control, and it seems most logical to take the fastest - not the safest - route in these situations.
If it were me though, I'd travel the wall.
A picture of the lift system implemented by the Survey Corps (Vol. 13, Chapter 51, 8):