Seeing as Everfrost popped out of recently defeated Frostifur, I had this idea. What if this material, which I have just collected from this monster, had real impact on how this monster acts? Maybe it could look more "frosty" than the others, or perhaps its attacks could cause stronger freeze. Similarly, Wolver with Bushy Tail would simply have bushy tail. I imagine low-star materials would only alter look and high-star would have impact on gameplay too.
This idea was born as explanation why you can't collect for example Bushy Tail from every Wolver. But apart from this, it would allow players to see what monster will drop what and also lead to creation of "champion monsters" in higher levels. Whether this is good or bad is up to discussion.
Seems like a good idea for the future, seeing as how slowly GH is releasing small amounts of content, this would take them years to make a reality, especially with the large amount of materials in the game. Maybe when they are done "saving up" as some assume they are doing, and focus on creating better playable content.