That's basically the idea of 'radical candor' (https://www.radicalcandor.com/wp-content/uploads/2016/03/rad...) and I think the main thing you're getting at.
For example, when a relationship needs to end (a romantic break up, a firing, etc.), there's a limited amount one can do to make someone feel good about themselves. To some degree our challenge in that sort of conversation is to limit our empathy for the purposes of doing the right thing.
In other words, when someone phrases something reasonably kindly and it's not taken well, we can't blame the speaker for the listener's hurt feelings. At some point, even if they're hurt, it's the listener's fault. That judgement can seem cold and maybe counter-intuitive. However, on the contrary, that's just an example of how empathy gets in the way of what is right.
Though I think those cases should be the exception to the norm.
As far as empathy getting in the way - I think in the firing example while managers often feel an urge to be empathetic in a misdirected way (i.e. "this decision is hard for me too") true empathy would be recognizing that if you were the one being fired there is no good way to state it and however difficult it is for you to fire them - it doesn't compare.
I guess to reframe it, it's more about thinking about how the other person will be affected and doing the best you can given the circumstance.
No, the empathetic thing in those situations is to end the relationship quickly precisely because you understand dragging it out will just damage the other party more in the long run.
I don't know. Sometimes the core of an issue is that someone messed up, bullied someone, didn't listen, or something along those lines. In some cases people should feel bad. We don't have to go out of our way to make them feel bad. They did it to themselves. And, to be clear, they shouldn't feel condemned. They should feel like they have a productive path forward. But glossing over important issues to avoid uncomfortable feelings isn't really kind in the long run.
Empathy is admirable and humanizing, and maybe we are short on it, but I'm not sold that it's always kinder.