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Closest thing I can find is Self-Care Epiphany, which is usually in the sense of running oneself ragged trying to help friends with big projects and never taking even the shortest break.
Interesting. Well, I was thinking of several examples and only really one even sort of fits into that. Maybe I'll bring this to Trope Launch Pad then.
^ The aesop of Soul revolves around this concept as well.
An Aesop that a character or characters need to stop doing everything so quickly and slow down to smell the roses or else they won't be able to get things done properly and/or will miss the little things in life that they can only enjoy if they take things slowly.