When I started working at Rainmaker, I was told that they didn't have the luxury of hiring specialists and that everyone was expected to be generalists.
My first task was texturing teeth. I had no idea what I was doing and I nearly lost my job. No kidding. Fortunately for me, as talented as the artists at Rainmaker are, I learned what generalists generally lack are decent animation skills.
Animation is just such a demanding discipline. Movement is something that is either right or wrong, not much room for artists who can “kind of animate.”
That said, there is nothing wrong with building your skills across the board. I don't agree with the idea that artists can't learn how to script, for example.