Despite what you may think, domesticating zebras is nothing new. People have been trying to domesticate zebras for about a hundred years. However, there is no zebra market, because zebras can’t be domesticated.
Compared to horses, zebras are pretty unpredictable. They can be very aggressive and even vicious as they get older. Plus, their body shape doesn’t take a saddle very well. Trying to train and ride a zebra is pretty dangerous.
Over the years, some zebras have been successfully trained, but as a group they just don’t lend themselves to domestication. Some animal trainers and breeders have created zebra hybrids, such as the “zorse,” a cross between a zebra and a horse, and the “zonkey”, which is what you get when you cross a zebra and a donkey.
So far there’s no specific purpose to creating zebra hybrids; they’re not stronger or more useful than regular horses and donkeys.