Actively not caring is not the same as passively ignoring or procrastinating. Walking down a supermarket aisle and choosing not to pick something up, instead of selecting a different one or not walking at all.
The simple finite nature of time, and within that the hours of a day where we are awake, with other people, and generous mood, makes caring and not caring, in their active state, an excellent compass for many different activities.
The act (not state) of not caring is discernment. It is the power to choose, navigate, and self-author. By self-authorship, I mean independent of authority (manager), monetary, or time constraints, navigating situations with personal foresight.
Caring is nurturing, with love and protecting from reactionary impulses, carrying through changing trends, habits and norms, because of the same foresight.
As a prompt, I ask you: can not caring become an active state? A decision you take to exercise discernment? Can you make a list of things you care about and one of the things you don't?