There is nothing wrong about "chasing the hands." In wrestling, that's called "grip fight".Chi Sao is about chasing the hands ...
In fighting, you will have 2 options.
1. striking method - use your hand to meet your opponent's face and knock him down.
2. grappling method - use your hands to control your opponent's arms so his hands/arms can't reach to your body.
Sometimes you don't want to break your opponent's nose. You just want him to stop attacking you. The 2nd approach is a much more civilized methods (less problem in court). It does require you to step into the grappling area.