* Discussing and ultimately making decisions
* Learning about how things work from people with a different set of knowledge than you
* Doing things which optimize for the understanding of other people after you, as opposed to optimizing for your own productivity in this second
Software engineers who do these things with low empathy end up contributing to the stereotypes about engineers who are unpleasant to work with because they don't consider other people.
If you mean CS in the academic sense, e.g. algorithm research, probably not much.
If you mean CS as in "occupation that involves designing and/implementing software" then I'd argue empathy is an integral part of being an effective professional. Empathy facillitates effective communication and ethical/moral decisions.
I think the idea that "all that matters is your code" is flawed. It's very short-sighted and narrow minded, and it does nothing but to artificially limit oneself. The world is bigger. You interact with other people and can have either a positive or negative effect on them.
Some of those other people might not know as much about CS, but might have other skills like design, marketing, management, etc. Empathy is a trait that helps one to appreciate and adapt to these differences constructively.
There was a time some while ago (as I blow mental dust off my college literature studies) when "passion" was not a word that carried wholly positive connotations. It came with implications of things like irrationality, moodiness, strong emotions, even violence.
Passion can be an asset if a person must maintain momentum in the face of hardships and competition. It can be the base for tremendously hard work (which is one reason I think employers like it). But, it could potentially be a liability too, if it drives a person to create conflict or inhibits teamwork. Depends on the role and the team.