Why is it "die Hausschuhe stehen and not liegen unter dem Bett"?
boots are taller than wide. This was perceived as standing up rather than lying down. It must have become grammaticalized and generalized.
Part of it is that we stand in and on shoes, as @VolkerLandgraf implied. Standing, and walking by extension, is the inherent purpose of feet equipment.
This applies to most set-ups that have a preffered standard orientation, like cups, except if notably two dimensional or amorph, and not to objects that tend to be moved or rather move on their own, like ships or dice. (Hence the joke about the running fridge, because it can run and stand at the same time).
In principle there's nothing wrong about liegen in this context, anyhow. In most cases a simple sein does the job as well.