The bag, tied on a branch, has been used for years. On plants where the air-layer takes all season to root, having a sealed rooting "container" helps retain moisture during the process. Figs root more quickly, and are more easily tooted in very damp media. I used 1 liter water bottles, slit, for easy removal of the air-layer when it is removed from the tree and potted up. I can add water as time goes by. So for me this is a simpler process than tying on the bags. the foil is used to keep the new roots from being sunburned. That is a requirement regardless of the rooting "container".
See Air Layers I have since reversed the bottles. I saw off the neck, and use it for the bottom of the air layer. I cut the bottom of the bottle off which becomes the top of my rooting container. Sawing off the neck is easy. Trying to cut a hole in the bottom of the bottle is difficult because that is the thickest part of the bottle. I also use smooth sided bottles, now. Easier to get the air-layer out of the bottle, and my neighbor "produces" lots of them.
In the end, it is all about what works for you, what is easy for you, and what follows the basic principles of rooting (balance of moisture and oxygen in the rooting zone).