As someone mentioned in a previous chapter, the greatest punishment for the princess would be to get raped by common townfolks.
She wanted to bear the children of the prince, because he has good looks, and she wants a beautiful child.
But if she were to be raped by some poor, dirty, nowhere near attractive commoner, she could say goodbye to a beautiful child most likely.
The early chapters had a great opportunity for it when the hero torn all of her clothes, stripping her completely naked in public.
I always despise and hate rape, and avoid every single manga that has it, but I'd like to see that happening here.
I wouldn't feel bad for the princess in the slightest.