A few thoughts.
I really don't know if empathy is entirely natural. It seems that to some degree we are taught to stop, consider others feelings, and I have no problem with that personally. Quite the opposite, I'd rather live in a world where people are aware of each other, at least some degree.
To me empathy has two parts. Being able to stop, consider how someone else would feel if we were in their shoes, plus also to have a sense of concern, to value their feelings, at least to a degree. Enough of a concern to act, even if the act is not to add to their hurt.
It's strange because we might have learned that empathy means to 'feel bad' for others, but there is no reason why empathy cannot also include feeling happier, positive, etc., when others feel that way.
Is there a cost? I suppose so. There is a risk that we might put someone else' feelings before our own, or just find it tiring to consider their feelings. It took me a long time to learn that empathy can go too far. That you can end up putting your own wants/feelings as 2nd place, and that's not right either. Imbalance indeed.
Is there a benefit? I think so. I really would rather live in a world with people who treat each other more or less how they want to be treated, and without empathy often what happens is people take what they want in the moment, even if they'd feel it unfair if the situation was reversed.