I'm looking for a phrase for the situation where the person responsible for seeing a task is done is the person least likely to do the task themselves. For example you wouldn't make Bob responsible for ensuring everyone washes their cup because Bob is the worst culprit for forgetting to wash his own cup.
I feel like "Choosing the fox to guard the henhouse" is not quite right as there is malice and/or cunning implied in what the fox would do in the henhouse.
Is there a phrase or idiom for choosing a person who is inept or ill suited for the work in this way? The subject of the discussion isn't stupid, just the opposite of the person you want for this task.