Soy milk compared to other bean milks
Its all about protein.

Protein content (and to a lesser degree, fat) is what will determine the yield when making curd from milk. Obviously it is also important for its nutrition.

Soy has almost double the protein of most other beans. It is around 17% vs 9% for most other varieties.
http://www.healthaliciousness.com/articles/beans-legumes-highest-protein.php

Because of its high protein and oil content and high yield it has become an agricultural staple. Because of this, as saj14saj said, it is very inexpensive at an industrial scale.

For these same reasons it has also been important in Asian diets for centuries. Soy milk also has a tradition behind it that I assume would make it easier to market than other milks.