When I was riding / racing in the 70s, all my bars were wrapped top down. I had one set of bars (can't remember the brand) that had sort of a reinforced center where the stem attached. It had square edges that were, oddly enough, about the same thickness as wrapped bar tape (the cloth kind) so the top end of the tape was the same diameter as the center of the bars. Never once did I have any fraying or unwrapping of the tape.
The only reason I wrapped my current bike bottom up (with tape at the top, which I still think is ugly) is because I have a bar end Di2 junction, and it sort of requires taping in that manner.