Armies are combined arms, with few exceptions (Mongolian horde, perhaps), they didn't have just a single unit type. But armored heavy cavalry (with stirrups) wasn't some kind of weird sociological hang-up of European nations, it was a very effective unit type to have in your mix, such that societies were "willing" to spend significant resources in supporting the existence of that unit.

Here "willing" really means, "subjected to competition pressure such that societies that didn't support heavy cavalry units were for the most part militarily bullied into either annexation or standing up their own heavy cavalry support system."

That lasted until the technological realities of war changed (sufficiently-advanced firearms), at which point quite rapidly those societies stopped fielding heavy cavalry, which is another data point that this wasn't some kind of peacock display from nobles.