In my humble opinion, empathy is very important for a writer. Being able to put yourself in the shoes of each of your characters. The ability to ‘be’ them, one after the other, is a definite advantage when it comes to writing down convincing descriptions of the internal workings of those characters and eliciting the emotions you want from readers.
Readers love well rounded characters, realistically flawed, motivated and human. We love to see them overcome impossible odds and get their well deserved just deserts. It gives us hope that we too can fine our happily ever after.