I have no expertise here, but I recall that Jarod Diamond's book Guns, Germs, and Steel claims that almost all wild animals lack a certain set of characteristic

I have no expertise here, but I recall that Jarod Diamond's book Guns, Germs, and Steel claims that almost all wild animals lack a certain set of characteristics that are essential for domestication. These include the ability to breed when living outside the wilderness (elephants lack this) and to be made tame so they don't attack humans and can be trained for useful work (zebras lack this). Also, it seems to me that people would not put the effort needed for domestication unless they thought the animal could fill some important niche that none of the present domesticated animals does.