There are already companies that use packaging made from formed paper and sugarcane. I would be interested to see what mycelium packaging offers over this.
I believe the mushroom packaging is more like a foam, so it may be able to better protect products. Additionally, it may have a more "premium" feeling/appearance vs. pulp packaging.
In the old days, wood shaving and even popcorn were the packing material of choice.
The reason styrofoam is used is because it's cheaper (main) and it doesn't decompose when wet.