Why are communciation protocols presented as Stacks (vertical) rather than as a conveyor belt (horizontal)?
When an OSI (or other) protocol stack is presented one aspect is that each layer on a system effectively talks to its peer layer on the other system. With the stacks vertical these layer-to-peer-layer relation is horizontal, which feels better than the alternative (vertical in your proposal).



Another reason is that conceptually the lower layers are 'closer to the hardware', hence 'lower'. 

In descriptions of other layered systems it often happens that one layer consists of independent parts, depicted side by side. Rotating such a picture 90 degrees does not feel right, probably because we want to talk about one layers as 'built on top of' another.