You are correct that caring is important - but it also isn't your responsibility at the end of the day. If you don't care you're doing it wrong - if you let it eat you up inside whenever anything goes wrong you're also doing it wrong.
Work-life balance is mostly talked about in terms of time commitments but there is also an emotional commitment you need to balance. It's unhealthy to be too far in either extreme and, especially folks that are naturally empathetic, should be more wary of falling into the trap of overinvesting in a workplace and suffering mentally for it.
If you go somewhere 8 hours a day, you'd like that place to matter to you. Anything else is just depressing.