Related to "caring" is the concept of "compassion". Which, etymologically distills to—to feel with…
Just as you've pointed out the impossibility of scaling "care" to match objective reality, it is equally impossible to scale "compassion", regardless of whether one erroneously thinks of themselves as an "empath".
My observations and self-awareness have revealed an uncomfortable and embarassing truth. Sometimes care, or compassion, can be fueled primarily by the desire to eliminate the unpleasant feelings caused by witnessing suffering, than by the desire to eliminate the suffering.
False compassion, in this sense, is focused on the negative effects of suffering experienced by the one observing the suffering. Those exhibiting false compassion will be like some of the examples you cited in your essay who are moved to act for primarily selfish reasons. (Acting from guilt is rooted in the selfish desire to remove the guilty feelings, for example).
True compassion is focused on the cause(s) of suffering and the negative effects experienced by the sufferer. It will work to address the root causes knowing that solving those will solve the suffering and all the negative effects as well.
Perhaps this subtle difference is obvious, but I submit it in hopes that it will shed some light for a few.
Once again, thank you for an inspiring essay. We do well to remember that a good life is one in which we do all the good we can. Best for us all to find out what that means in practical application. Your essay is an excellent nudge in that direction.