It would be way more logical if she ate only few products and refused to eat anything else.
That would still lead to an awful health condition over time, but that's at least something.
Like, she could only eat things she never ate in her childhood since she hated it, for example.
That would also make an interesting storyline, where MC is trying to invent new dishes out of these few ingredients for her sake (in order to brighten up her mood or maybe even to overcome disgust) and at the same time try to put some camouflaged side ingredients into her food.
Oh damn it. This is so much more interesting and believable, that now I almost want to draw a manga myself on that idea.