The hero under the spotlight
Wave's backstory brings back a recurrent message of CB, learning to respect each and every role.
We hear of this first in sick day, as a part of Deacon's character arc as he learns to stop chasing the hero role and starts doing his best in whatever role he is assigned.
It comes up again in Perfect Halo, when Chase and Buddy step down from the stage and acknowledge that it's unfair to not let others have their chance at being the hero.
It is a message fundamental to the key magic harmony, a message fundamental to understanding of stories. One might assume it is something a stage actor would know, and appreciate. The beauty of all roles working together in harmony in creation of art.
But Wave, in the haze of his vanity and his lust for youth, never understood this. He doesn't respect the other roles. He couldn't tolerate stepping down from the hero role to give the chance to younger generations. (direct opposite to Perfect Halo, where Prunella was quite literally lifted up to have the role)
All Wave cares for is the spotlight.
I have to say, Wave might've fooled us all, but that only makes him a master manipulator, not an actor. Acting is an art, theatre is an art. Wave has neither love nor respect for it. Despite his century old existence, he never understood it.
Theatre was yet another tool for him to use to gain that golden spotlight. Just a medium to find more voices which would praise his supposed beauty.
He wasn't much of an actor. A good actor doesn't need the role of a hero to shine.
Edit: credits to @wistaliia for the green edit. I'll keep laughing about this mixup for quite some time