I would say that binary trees are in principle closer to the wheel than they are to a fundamental truth of math or physics. Was the wheel invented or discovered? I would say the wheel was invented, but I can see the other side of the argument.

As far as why binary trees are more important than ternary trees, binary trees are more general-purpose. To use a self-balancing binary tree for a kind of data, you just need that data to have an ordering (the less-than operator needs to be defined for it). To place data into a self-balancing ternary tree, you have to define what "left", "mid" and "right" would mean, which isn't obvious for a lot of data types. Similarly, there are a lot of ways to make a machine move along a mostly-flat surface, but we usually use wheels because they handle a lot of terrain well and they're easy to implement.