I used to think that then I burnt out. When the manager does nothing but the crap, the manager is going to leave. The proper way is to distribute the crap evenly.
The best managers I've ever worked for have all, without fail, worked daily to keep as much nonsense away from the team as possible. The worst have either only been concerned with their personal advancement, or would just make the team basically fend for itself.
It's those worst ones who end up in upper management precisely for those reasons.
And thus the rain of crap continues.
I agree that it isn't objective, but how is believing it is disingenuous?
This is true of "crap work" (i.e. stupid bugs, wading through documentation) but not of the crap external to the team. Your job as the manager is to deal with it all. You can either work to slow it's generation or suck it down, but it's all on you.