The person who explains a process clearly has already done part of improving it.

You cannot explain something clearly without first finding out what it actually is. Writing the steps down forces the vague parts into the open: the stage nobody can justify, the approval that exists because of something that went wrong years ago, the loop where work goes backwards. Half the improvements come out of that exercise before anyone has set out to improve anything.

Take a process you know well and write it out for a newcomer, in order, without smoothing over the awkward bits. The places where you find yourself apologising as you write are the places to change.