The list of domesticated animals is actually quite small, and if you further narrow it down to mammals which can produce milk, there aren’t that many options. You would then impose further criteria, such as:

• must be a large animal producing enough milk to be worth milking
• must adapt to a range of climate/geography so it can spread wherever humans go
• must be docile enough to milk without risking injury
• must be cheap to feed and maintain, to reduce the net cost of the milk
• must be relatively easy to prolong lactation to maximize milk output
• preferably a herd animal so you can scale up production

If you apply such criteria, cattle are pretty much the only animals the stand out. Horses are large, but much more expensive to maintain and more prone to disease. Camels are large, but not very docile, not as adaptable to the range of climates that cattle thrive in.

One thing to understand is that no animal was ever domesticated for milk. All animals were domesticated for some other purpose, and milk only became a secondary product much later. Cattle were domesticated 8,000-10,000 years ago in the Middle East and in India, as meat animals. It’s not until around 6,000 years ago that we have the first evidence of dairy use (cheese) and not until 5,000 years ago that we have evidence of the direct consumption of milk. Similarly, goats and sheep were domesticated as meat animals. Secondary uses for wool or milk came thousands of years later.

So the situation was that humans never picked animals to domesticate on the basis of milk production, they picked the animals based on other criteria. Once the animals were already domesticated, milk became a secondary product. All these animals have been used for secondary milk production, including horses, camels, llamas, goats and sheep, etc. However, some provide better returns than others, so if you want to make milk the primary product, you would pick only the best performers, which are cattle, followed by goats/sheep. Cattle (including cows, water buffalo, yaks and other bovids) wherever cattle can thrive, and goats/sheep in places where they can't.

Breeding for particular traits is a long and complex process. It’s taken thousands of years to produce the current breed of cattle that have such high milk yields. Putting that much effort into another animal may not be worthwhile. Even supposing you could produce a breed of camels optimized for milk production, why would you? Cows already serve that role for historical reasons. Over most of the globe, it’s much easier to adapt an existing breed of cow to your particular climate and feed resources than it is to optimize some other local mammal for milk production. A lot of effort has gone into cattle, and most people would rather leverage the work already done than reinvent the wheel.