Blake becoming a huntress actually makes sense. She was disappointed in the White Fang, but this does not mean that she immediately accepted the point of view of her parents, so she could not simply return. It makes sense for her to seek both personal power and reputation to be able to advance her vision, even if she is not yet sure what it is. After all, hunters have a significant reputation, people are more likely to trust them and listen to their words, both humans and fauns. Of course, this will not solve the problem in itself, but it will provide more opportunities for solving the problem.
It wasn't necessarily the only or best path to Blake's goal, but it wasn't a stupid or illogical choice.