People work differently for someone who would never ask them to carry what they refuse to carry themselves.

People calibrate their effort to what they see at the top. Someone who takes the unglamorous work, the late problem, the awkward conversation, establishes that these things are shared rather than assigned downward. That single fact changes how a group responds to being asked for anything.

Find the task you have been quietly routing to others because it is tedious or uncomfortable. Do it yourself once, visibly and without comment. The effect on willingness lasts much longer than the task.