Well, in deathgame,
- I used it to effectively simultaneously link many stockpiles to many workshops at once: Most significantly in mood workshop burrow, where it linked something like 20 stockpiles to 10 workshops each, an action that would have taken otherwise something like third a hour. In case of a mood, all I had to do was to add the modded citizen to burrow and unforbid things in it, and unlike with linked stockpiles didn't even have to forbid other workshops to prevent those from being claimed. (Have to remember to remove them later, though.)
A different fortress could use similar application to ensure kitchen/still brews/cooks a mix of drinks, for instance.
- Further used it so that a decorating jeweler and forge could keep decorating that same crown without waiting for hauler to come to move it to desired linked stockpile and being cancel-spammed in the meantime.
Other applications would be using it with, say, a loom - in the caverns, ensuring that nobody important gets bitten by a cave spider or worse.
More like the first example, any time a workshop produces a good that is used in another workshop - with loom, again: draw from farmer's workshop without needing a hauler to haul the thread to a stockpile or needing a hospital store thread you want to keep for injuries in the hospital bag/box.
Even if you're linking just 1 workshop to 1 stockpile, a burrow is more amnesia-compatible; there's no way to get a list of all the stockpiles linked to a workshop without going through all the (possibly hundreds) of stockpiles you have. Very useful if you look back few months later, or perhaps pass the save in succession fortress.