That has causation backwards: nobles weren’t cavalry because cavalry won battles*, but because cavalry was so expensive that only nobles and well funded centralized states with professional armies could afford them. You not only had to train the rider from a relatively young age but feed and support all the horses they’d need - armies rode in with at least three horses per rider on campaign to keep the horses from exhaustion (not including all the ones they’d train on). Supporting cavalry easily cost 5-10 times as much as supporting an equal number of infantry.
* Which it very often did, but for unrelated psychological reasons.
Cavalry won battles in societies that favored cavalry. If your society was built around elite warriors, your army probably relied on cavalry, because those elite warriors wanted to be individually as effective as possible. But if the state was responsible for raising the army and there was a middle class with sufficient combat skills available, infantry (such as Roman legions or mercenary pikemen) was often more cost-effective.
War elephants also beat cavalry in sufficient numbers. Various European, Mediterranean, and Middle Eastern powers tried them but found that they were not cost-effective. South and Southeast Asia thought otherwise.
This isn’t entirely down to arbitrary cultural preference. Terrain and enemy composition are relevant. All of the cultures that used war elephants successfully lived and mostly fought in elephant habitats. Likewise, cultures on or close to the steppe had much more of a cavalry focus because cavalry was so much more effective there. When the Romans went east, they didn’t stick to their heavy infantry, they developed cataphracts. And their eventual conquerors, the Turks, replaced most of their traditional cavalry with infantry as they expanded westward into Europe.
It's less about cultural preferences and more about fighting with what you have.
If you have a feudal society based on personal relationships between the elites, you probably can't raise large bodies of heavy infantry. You don't have the people trained to fight in formation, you don't have the resources to equip them, and you don't have the capacity to organize them. Instead, you have the elites, who are often well trained and equipped. The elites have their personal retainers, who are pretty much the same. There can be some mercenaries if you can afford them. And then there are commoners who have to fight for various reasons but often lack both training and equipment.
Elephants used to be native to North Africa, until the Roman Empire drove the subspecies to extinction. Carthaginians, Romans, and some Macedonian kingdoms used them in war. Persians and other Macedonian kingdoms imported elephants from India. But none of them fielded more than tens of elephants at once, at which scale infantry was capable of countering them. Some contemporary Indian kingdoms found it practical to have hundreds of elephants on the battlefield, which was qualitatively a different situation.
You fight with what you have but then sometimes you lose to someone who has a better army than you do and disappear from history. So in the long run you end up fighting with what actually works in your terrain. And I think it's very interesting that horses, who are only really indigenous to the steppe, ended up proliferating over the entire earth in a way that elephants did not. Hundreds of elephants on the battlefield sounds great if you can feed them though!
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.
>It'd be very silly to favor something that doesn't work, and any attempts to do so probably wouldn't last long.
What are your political beliefs? Because this argument applies equally well to cavalry as it does to communism. Would you seriously claim that all stupid political beliefs are new?
Who is “you” in this case? Is you the Roman state or is you a random noble trying to curry favor and glory?
The former supported cavalry because it won battles but the latter did so because it earned them prestige among their peers. It also helped them feel powerful when they rode into battle literally hoisted above the common foot solider, as if they were closer to the gods.
There's a notable technological divergence between the Roman and the noble - stirrups that make cavalry charges possible. Roman cavalry were usually lightly armed and armored and had a very different function on the battlefield.
Also as I recently learned from Lindybaige video, war horses themselves were “one shot weapon” - you would train one to do a “cavalry charge” and would not be able to repeat it with the same horse. So in essence, even more expensive!
Well, in the Bhagavad Gita and in Ramesses' inscriptions, chariot archers did win battles, were the heroes, and were the nobles. There's some speculation that changes in weaponry making this approach obsolete were the main cause of the Bronze Age Collapse. (Devereaux is writing about more recent wars, but archer volleys from chariots seem even less likely.)