Ulco, a warped simple shape will behave similar on a wall as in your 'warp on Y' example?
WAS, 'world position' does not equal 'final position'.
I can see why you think so, but they have a different meaning in a different context.
'World position' is perhaps better called 'world space'.
World space is non-deformable/non-warpable. It's the ground coordinate system on which all other (deformable) texture spaces rest.
Within world space you have object space, texture space, geometry space (terrain) or cloud space.
These are different types of coordinate systems for different elements of the scene.
World position in the transform shader converts the input 'space' to world space.
The 'final position' applies to the context of the terrain and although the final position of a point in your terrain exists within world space ultimately, it is not 1:1 connected to 'world position' or 'world space' in this context.
If you want to warp a simple shape and rotate it to be 'standing upright' then you need to respect the hierarchy of texture spaces.
As Ulco already explained you first need to warp and then rotate it in world space mode.
It's just that his example is not entirely convincing, although the settings in the nodes are correct, but those are not shown.