They said DEVIL because it sounded cool and fit in with the game...when they say Rage of the Gods in GoW, you think the gods come down and use their own fury? NO!...it's a heightened state of power and is the same thing in DMC
Let me think:
Kratos who is half human-half god. Killed Ares and became God of War.
You earned a technique gameplay wise called "Rage of the Gods".
Do i think Zeus, Aprhodide, Athena, Hera, etc will appear and smite the enemies? No.
Do i think Kratos will transform into Zeus or a other god? No.
Is Kratos god of war? Yes.
What does that mean? It's a technique.
Does it make sense that Dante a half demon half human should look like a demon? Yes.
How is it done? Through Devil trigger.
Does a demon look like the Devil? Yes, search "Devil" and compare pictures of people portraying the Devil with DMC Devil triggers and demons.
If a character is half human- half wolf = a werewolf. Is it more right to make him achieve a heightened state gameplaywise but no transform into a werewolf? No.
The transformation grants the power.
Of course DT is a heightened state. But that heightened state is provided by the demonic blood in Dante.
If it's not provided by the demon blood Dante has in his veins. Then what is providing it?
They called it "Devil trigger" to make it sound cool? I guess they called also the game "DEvil May Cry" to make it sound cool, and it has nothing with fact the game is about demons.
If a demon is just a human looking creature then why is all the demons in DMC devil looking?
Your logic that it's just a heightened state and that's only point of Devil trigger is flawed.