I don't really have a lot of empathy for 'random' people, so I can't comment on that, but if I had no empathy at all for a friend, family member or similar that's suffering, that'd be unhealthy. Normally, there's a connection to those people that makes us feel with them.

Having too much of it for those people is something I sometimes struggle with, for me it's mostly related to emotion regulation in general. So maybe looking into regulating the emotions that come up could help.