I have used cage transform in the past, and it worked fine.
I am now in a situation where I can not cage-transform an object.
Instead of transforming, I can only create a cage, and when I finish the cage, it automatically transforms.
I have uploaded a video here.
What am I missing?
I don't see it transforming. When the cage is closed, something happens, but the image is not changed and the cage remains. You can from that point alter the cage and this will alter the image. This is indicated/controlled by this widget int the tool options:
By the way, if you are mapping a rectangle to a 4-points polygon (or vice versa) using the perspective tool can be more accurate ad possibly faster.