Hello. I apologize for the late reply.
The thing about using a stone to evolve an already-evolved puppet is that its moveset is preserved, allowing you to get movesets you normally shouldn't be able to get, such as Aeroblast on Attack Utsuho. I know it feels like a weak reason, but I just don't want to make the game too much easier than I've already made it over time.
Basically, it goes against my vision, and I'm stubborn.