Comment by WJW

Not OP, but there's a nuance. In general there's nothing wrong with wanting to be useful, but it is definitely possible to take it too far.

If you get sick and need care, you are typically not "useful". But that doesn't mean you instantly lose all value. I've had colleagues who would feel almost physically ill if they were somehow not able to respond to an incident somewhere, even if they weren't even on call at that point. Almost all of them burned out at some point and were no longer able to respond to anything, even if they'd wanted to. That's not healthy, and it weakens everyone in the long run.

Resting without guilt comes from the realization that you cannot keep the world running all by yourself. Let others pick up the work when you need a rest, so you can shelter them when they are down.