I think many long-time managers can recall some time were they really just put up busywork for them to not have to deal with that team member. It's not the best solution but sometimes it eases political conflicts.

I wouldn't recommend this. As I mentioned in a reply to a different post: A good idea, widely visible, must be addressed by leadership. Failing to do so makes you look incompetent as a leader. That doesn't mean it has be implemented immediately, but it needs to be referenced in the larger plan, along with a rationale.

I think that's unfair.