I think of it as the opposite: there exists a Lie group of spatial rotations, so we want to use it, and we found a relatively convenient notation.
There are many other kinds of 'complex' numbers (http://en.wikipedia.org/wiki/Hypercomplex_number) - but you probably won't hear about them outside of mathematics and physics because they're less useful.
The same applies to 2d - the SO(2) group exists; we map it to the complex numbers because it's convenient to do math with.
As much as anything, it is a chosen property of the system.
If you want to insist that mathematics is discovered (rather than invented), you can still say that this particular decomposition of vectors is prevalent because it has useful properties.
