Random shuffling of songs usually refers to a randomized ordering of a given set of songs, so the same song can’t occur twice in a row if the set only contains unique items. People don’t usually mean an independent random selection from the set each time.

>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).

You could think of it as wanting your desire to hear the song again build up to a sufficient level to make it worth a relisten, sort of how a bus driver might want potential passengers to accumulate at a bus stop before picking them up, and therefore delay arrival. Very plausible to me that a good music randomization would have similar statistics if you phrase it right.

If the list of songs is random shuffled, you can only hear the same song twice if there is a duplicate or if you've cycled through the whole list. That's why you shuffle lists instead of randomly selecting list elements.