It doesn't seem too unusual to me, and I don't think very many people will share your view that it is "immoral".
At least in US universities, the professor has quite wide discretion to determine the grading policy, so long as it is clearly described in the syllabus and applied equally to all students. This seems well within the realm of acceptability. Schemes based on some weighted average of assignments and exams are the most common, but I've certainly seen schemes where you have to have a minimum grade on certain components to pass.
As far as "legal", laws tend to avoid micromanaging academic matters, so I would be very surprised if there is any law that would forbid this. University policy is more likely to address it, but again, I'd be surprised if what you describe wasn't allowed. I don't think you will have any success trying to fight this at a higher level.
As far as it being unfair to students who are poor test takers, bear in mind that in many educational systems, it is common for the course grade to be determined entirely by a single exam. Rightly or wrongly, there's a long history of evaluating students by exams, with the attitude that students who aren't good at taking tests need to find a way to get better at it. (Accommodations may be made for students whose test-taking difficulties are due to a diagnosed learning disability, but this usually means adjusting the exam conditions rather than de-emphasizing exams in general.)
You are certainly free to express your disagreement with this policy, either directly to the professor or in anonymous evaluations, but it may not be possible for her to change it after the course has started. This could be seen as unfair to students who have been setting their priorities accordingly.