Having looked at some images of people riding cows, I immediately notice that cows are much lower and with shorter legs than horses. Someone riding a cow would be at an immediate disadvantage in height and speed to a horse rider, not to mention the increased agility of the horse. So even if riding a cow were practical, it would be an inferior option to a horse. Quick Googling says that cows run up to 20mph, whereas a horse gallops at ~30mph with a top speed around 45mph.
I say “if it were practical” because most of the cattle I saw being ridden were Texas Longhorns and seemed to be more of a novelty act than anything else. But Texas Longhorns are a relatively recent breed (from a history of war standpoint, anyway) and whatever traits they have may have simply been missing from the local cattle, thus making them a poor choice for any nontraditional bovine roles.
Horses have the same herd and run away behavior. When horses attack, they generally try to bite or kick. When cows attack, they try to gore and send the person flying.
That’s simply a result of human selection. We want fast horses and fat cows. A wildebeest isn’t much shorter than a horse.
But you don’t want the animal you’re mounted on to be engaging directly with the enemy. With horse cavalry, the riders don’t encourage their mounts to kick or bite the enemy. Neither would you really want a war cow to be goring someone. The animal’s twisting and thrusting would make it very difficult to stay on. The enemy might go flying, but you would too.
Mounts are for transporting humans so they can engage other humans with weapons. It wouldn’t be possible to train a cow to attack a human or another cow reliably enough to be worth it, especially at the risk of becoming dismounted yourself.
For one thing, wildebeest are antelope, not bovines so using them as your guide to what a war-cow should look like is misguided.
Colibri hit on the point that the ability of a steed to run into things is down the list from speed, agility, ability to follow commands, etc. A cow is simply an inferior choice to a horse for those things. And for all the time you could waste trying to turn a cow into a horse, the other guy has horses.
I disagree with your assertion that you just breed it to look/do what you want. There is something inherent about bovines being broad and shorter – that’s what bovines naturally look like. Look at water buffalo or zebu or yaks or musk oxen. We may have capitalized on these traits but we were taking the path of least resistance based on what we liked about the beasts. Taking a short, fat dumb animal and making it fatter is easy. Taking a short, fat animal and breeding it into a tall, lean animal that obeys rider commands is a lot different. And there’s no reason to assume that even with dedicated efforts you’d get what you want; plenty of animals prove unsuited for tasks because of their disposition (see earlier remarks on domesticating zebra) and even if you found a taller, leaner cow that doesn’t mean it’ll ever accept a rider or that a slightly more intelligent cow will keep those traits as you try to give it the body of a horse.
In short, cows are just inferior choices as steeds in every aspect beyond running into things, “running into things” isn’t the principle job of a steed anyway, and there’s no good reason to assume you’d overcome these issues by breeding.
“Bovine” refers more to Bovini than to the entire Bovidae family. You don’t, for example, usually hear “bovine” used to refer to sheep or goats. Wildebeest belong to Alcelaphinae which is a different subfamily within Bovidae from Bovinae and what we consider “bovines” are a subtribe even within Bovinae.
In other words, wildebeest ain’t cows.
Edit: Typing “Bovine” into Wiki redirects you to “Bovinae” which doesn’t include Wildebeest.
