If only it was as simple as you think.
This could easily be my dd, her diet is very similar, each day is a battle with me trying to get her to eat something different, she has severe sensory issues around food, she has Aspergers, she has hypermobility and low muscle tone which effects her swallowing and gag reflexes. He diet is mainly bread, cheese and potato, she won’t eat meat, she gags if I put a vegetable on her plate, dinner times often end with her crying and feeling sick. I have asked for help many times through GP often to be told “let her eat what she likes” or the other extreme “let her go hungry”, neither really solve the problem as dd will happily not eat rather than look at a vegetable. My dd has bad eye sight, she has problems with her bones, she’s pale and is gaining weight but no one will help us.
You can’t force a teenager to take tablets/supplements, you can’t control what they eat all the time. All I can do is cut out carbs by not buying them but then my dd doesn’t eat, we have swapped white bread for brown, use lower fat cheese and occasionally I can get her to drink a smoothie but getting her to eat vegetables or meat is unlikely to happen.