If those are your reasons for caring about complex analysis, then I'm not sure to what extent I can convince you to care about SCV.
But here is why I like SCV: I like multivariable calculus, and I like complex numbers. I've always wondered what would happen if you put the two together. And apparently pretty wild things happen (compared with either the single-variable or real-variable case).
I'm also really interested in complex geometry. The local theory of complex manifolds involves SCV.
One final comment: Your reason (1) for caring about holomorphic functions is in fact my reason for caring about harmonic functions (for which I would otherwise desire motivation).
