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.
Having a unit type in your toolkit is one thing, and expecting it to play a decisive role in battle is another. For example, Alexander's heavy infantry was supposed to anchor the enemy in place as cavalry won the battle, while Roman heavy infantry the primary fighting force.
Mercenary pikemen ended the dominance of heavy cavalry in Europe before firearms became common. But that didn't make heavy cavalry obsolete, and neither did firearms. Cuirassiers had a prominent role in the Napoleonic Wars, and French cuirassiers actually wore their breastplates a few weeks into WW1.
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.