How can I mass cage quickly?

I believe this is due to the cage generating only a single animal hauling job at a time. While pastures can create multiple animal hauling jobs at once (one for each square in the pasture?), cages will only create a new job, for a different animal, after the previous job has been completed.

If getting all your animals in different cages is not a problem, you can split your animals in small groups and bring each to a different cage. Since each cage will be handling the hauling jobs separately, it becomes possible to have multiple dwarves caging your animals at the same time.