>For example, you'd not want hear the same track twice in a row, even though this is bound to happen in a strictly random shuffling.

Why would it be? A random shuffling of a unique set remains a unique set.

It's only when "next song is picked at random each time from set" which you're bound to hear the same song twice, but that's not a random playlist shuffling (shuffling implies the new set is created at once).

a new ordering, not a new set