As I explained in the answer to the question The metric of the expected difference of random variables, I don't see any reason for closing it other than simple misunderstanding (to put it mildly) on the part of those who did it. [In spite of OP's disclaimer, what is the starting point of a very interesting recent mathematical development was mistaken for the trivial definition of $L^1$ metric.] If this is indeed the case I invite them to reopen the question, if not then to give their reasons.
Edit: The question has been reopened. Those who feel it should have remained closed are invited to give their reasons.