In Little red riding hood was the wolf actually bad?

When researching my previous question on little red riding hood I noticed something interesting. In the English version the wolf is referred to as "The big bad wolf" but in the welsh version it's "The big black wolf". It would be interesting to see how he's portrayed in different languages.

But it got me thinking. Did we leave out the "bad" Part because the wolf isn't actually bad? After all he's a predator just trying to get a meal, that doesn't make him bad.

Thoughts
In Little red riding hood was the wolf actually bad?
In Little red riding hood was the wolf actually bad?
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