Caveat - IANA Zebra expert…
I have worked (briefly) with zebra and other hooved stock in a zoo setting. And I once knew, and occasionally interacted with, a privately owned “tame” zebra that would pull a cart. (On good days, anyway.) And, allowing comparison, I own horses.
Like most equids, the basic zebra reaction to threat is flight. Most of the time, they will simply run away. Occasionally though a challenged stallion or a mare with foal at her side will display aggression-- toward a keeper, or an interloping dog. They are quick, nimble, and powerful, and can stomp you flat. Zebras therefore have a reputation as “potentially quite dangerous” with zoo keepers.
That said though, I hardly think this trait would be sufficient to prevent domestication. The real barriers to domestication, as stated upthread, are time, opportunity, and economic benefit.
To domesticate an animal, a number of breeding individuals must be kept isolated, and selectively bred for a large (but admittedly undetermined) number of generations. Simply maintaining this herd presupposes that the society has sufficient space, technology to maintain adequate fences, and a year-round source of animal feed. The un-domesticated “starter herd” cannot be simply ‘driven’ to another pasture if the first becomes over-grazed. The African savanna, with its seasonal cycle of wet and dry and the concomittant seasonal cycle of grass versus no grass strikes me as a poor choice for such an endeavor. If this first hurdle could be overcome, perhaps by fencing and cross fencing a truly huge area, then a beginning herd could be maintained.
But since domestication could at best be only a dimly perceived long term goal, the herd must provide some immediate benefit in order to justify the effort. Presumably this would be a ready supply of meat without the necessity for hunting and possible long distance travel. So we already know what will be done with culls, and can assume that culling will take place. How large a herd then is needed to support the human population? Or to supplement a supply of hunted “wild” meat? Is that fenced pasture really big enough?
And how often will there be ‘bad years’, years of drought or famine, in which the entire herd will be eaten or simply perish, negating all previous selection for domestication and necessitating starting over with new wild stock? Even if such occurs only once in a century, or even longer, it would prevent successful domestication through selection. Again, Africa seems to be especially problematic in this regard, mediating against domestication of zebra.
How often might a pride of lions, or a prairie fire, or a herd of elephant, or some other scenario cause the herd to escape their enclosure? The larger the necessary pasture, the more likely such a misadventure becomes. And again, even if this is a once in a century event, the result is back to square one on the domestication front.
To me, there is no surprise in the fact that zebras were never domesticated. Any measure of aggression seems trivial compared to the other hurdles that must be overcome. Historical African aboriginal societies seem ill equipped for this effort.
Could some other, richer and more settled historical society, perhaps the ancient Egyptians or the Persians, have succeeded? Possibly, if they were willing to devote the necessary resources to the effort. One could envision a relatively small herd maintained strictly for the long term goal of domestication, not an immediate food supply. This could be maintained for maximum breeding production and minimum generational time, while being ruthlessly culled. Some hundred or hundreds of years of sustained effort should result in a fair measure of domestication.
But what would be the point? Is there any reason to expect that such an animal would be superior to the domestic or semi-domestic horses, donkeys, and other equids already available at that time? Or superior to such specialty beasts of burden as oxen or water buffalo? Or as easy to maintain for ready food supplies as sheep or goats?
Massive practical, logistical, and economic difficulties to overcome with specious potential long term benefit (not aggressive behaviors) equals null program.