Alright I guess we are slectively suspending some of the causes of domestication to see what could have happened.
Sigh. Condescend much?
No, not suspending some of the causes of domestication. Rather, playing with the variables, which is what this thread is all about.
For instance - elephants were independently semi-domesticated by at least four cultures - North Africa, Mesopotamia, India and North China.
In each case, elephants disappeared from the local economy. Why? A couple of reasons. First, although elephants could be tamed and used fairly easily and had major economic significance, the long maturation rates made domestic breeding a doubtful proposition. The preference was to harvest animals from the wild and tame them. When the wild populations were hunted out or displaced by habitat erasure, semi-domesticated elephants disappeared from the population.
There's also a secondary, but equally significant issue, in that elephants were effectively outcompeted as a draft animal by cattle. The working life span of an elephant was vastly longer than cattle, and the amount of work that an elephant could do vastly outstripped a cow. But if you compared the amount of work a number of cattle could do, and compared that with a single elephant, the equation changed... particularly when the feeding costs were the same. Cattle were also much more fluid - they reproduced fast, matured quickly, and you could adjust the working task by hooking cattle up serially to maximize your task to labour ratio.
So, how do you play those variables to get domesticated elephants? Any number of ways. Smaller, faster maturing elephants might have been more competitive (and I've read that the north african elephants were relatively smaller).
Or it may have been as simple as a culture determining that elephants were valuable enough that some deliberate effort goes into breeding.
Or you could have a situation where a local disease or parasite, like the Tse Tse fly prevents cattle from coming into use (as it did in parts of sub-saharan Africa).
Or a situation where an earlier and more consolidated domestication of elephants forecloses on the domestication of rivals.
This site is all about alternate history, or paths not taken.
Cattle, and much, much, much, later horses were domesticated because in one region, early agriculture took a specific path - it focused on domesticating field cereals or grains, in a region where that sort of domestication could spread far. Because we domesticated cereals and grains, grazers became the big domesticates.
But even in our own history, it's not the only agricultural model out there. It's not beyond arguing that had an alternate agricultural model achieved prominence - say a forest wetlands agriculture, a northern equivalent to tropical wetlands agriculture, that you would have seen the big browsers being domesticated - instead of horse and cattle, you'd get elk and moose.
It's not a matter of saying that we're going to suspend some causes of domestication with regard to the domestication of reindeer/caribou. It actually happened one place, and didn't happen another for cultural reasons.
Ostrich were not domesticated until the 19th or early 20th century, at which point there were a number of draft animals already developed and no need for it on that score. But conceivably, they could have been domesticated 3000 years ago, and served as a draft animal for a society which had none, radically changing the course of African civilization.
Hell, one could argue that the Horse could have been the first draft domesticate rather than cattle, and examine how that might have changed things.
Or that the horse was not domesticated at all, but simply hunted to extinction.
It seems to me to be presumptuous to blithely say that all that could have been domesticated have been domesticated. Whether an animal is domesticated at all comes down to a large number of variables.