This is some low performance team they must be managing. Interrupt-driven task allocation is inherently dysfunctional.
In a high performance team, it's more like managing a band. The manager is not the talent. You are Brian Epstein, not John Lennon. You enable the talent. You hire smart people, give them goals and the resources they need, then get the fuck out of their way. They don't take out the trash. You do it. Or hire a janitor, since it seems you value the task; that's someone who didn't need asking, because GC is already in their JD.
In a high performance team, it's more like managing a band. The manager is not the talent. You are Brian Epstein, not John Lennon. You enable the talent. You hire smart people, give them goals and the resources they need, then get the fuck out of their way. They don't take out the trash. You do it. Or hire a janitor, since it seems you value the task; that's someone who didn't need asking, because GC is already in their JD.