I think the way you pack and store your fabric depends upon where they will be stored more than the how. I love the idea of using fabric to wrap breakables. I've done that lots of times.
But I did have to store the entire house several years back and I was so glad that I packed the fabrics in plastic totes. The floor of the storage unit got wet due to a very heavy rain and things in cardboard got damaged. I had to throw out several quilting books.... hated losing those.
If you'll store in one place while being in another, you won't be able to check on things. Think ahead! Plan wisely.