Cute hack. I prefer hanging batting on the wall so I can roll off what I need, but this is a great hack if you have not got the wall space!
As for bugs...I totally forgot about wool moth until I moved our couch one day and found wool moths had eaten away an entire 1' square area of my very expensive wool carpet, leaving only the sisal part the wool is attached to. Tunnels all over the area. It took months to kill all the moths. We applied insecticide to the carpet and then dusted all our wool carpets top and bottom surfaces with diatomaceous earth.
The diatomaceous earth is a flour-like white powder made of diatoms, and is non toxic. Available in garden stores, bugs that come in contact with it get scratches from the very hard coral-like microscopic diatoms and that kills them.
This reminds me I have a whole roll of wool batting I need to check for carpet/wool moths!! I will unroll it and give it a dusting too.
The moths are very tiny, about 1/3 the size of pantry moths, which they resemble. I think they could crawl into anything that is not contained in a fairly fine net bag, a fabric bag or a sealed plastic bag.
In the old days, folks used mothballs, but they don't smell very nice and are probably not good for us mammals. Cedar was the other way to store woolen goods...hence cedar chests.