Well, I did a corpus search, and it turns out that in such short sentences like this one, it's about 50 times less common. So "probably less frequent" is definitely a massive understatement.
It's a beginner course's prerogative to reject unusual and rare word orders.
If you use Formal You, you cannot omit the subject. "Dlaczego się śpieszy" without "pani" is just "Why is he/she/it in a hurry?", and the subject would need to be known from the context.
I chose the right option, but if asked to translate the sentence, I normally would say, "Czemu pani się spieszy?". Is this also correct? If so, is one word order better than the other one and if so, why?