The battle seems lost at 14. In the early years though, picky as kids may be, they won't starve themselves. You can negotiate to such a point that they'll consume enough healthy food on the regular. If you always provide unhealthy alternatives these will be exploited. If you enable and pander they'll have nothing but garbage.

Of course not. I’m willing to bet it’s an issue with the parents actions over the course of a decade unless the child has severe mental disabilities. It’s impossible to believe an otherwise healthy 14 year old child would die by refusing to eat food other than carrots and chicken nuggets for weeks on end. Doctors may give answers but it’s up to the parents to follow through.

I was 18 when I was sent to a university hostel with a terrible dining system. My parents didn't give me a penny beyond what was required to survive.

Lo and behold, in a few months, I was eating terrible tasting mess food that I wouldn't have otherwise touched back home.

He's just 14. It may just take policies that are more radical than you probably like or endorse.

I do this to my kids. I don't know if it helps. (The older one is 9 who eats almost everything and a younger picky eater who is 5.) Getting them to try a wider variety of food is often tough since it is easy to fall back on the usual stuff. Occasionally I have new types of food, I would make a small bitesize and use all the powers I have for them to take the first mouth. If they swallow it without tasting, they get a second mouth of it. They have to describe the taste to me precisely in simple terms, e.g sweet, chunky, sour, like apples etc. Often when they have a conscious bias, e.g. the younger one dislikes anything that resembles white creamy sauce, they will say it is "yucky". Yucky is not a taste descriptor. I sometimes add things they like e.g. bits of chocolate. My goal is to encourage them to focus on the taste and make connections like "this ugly piece of food will taste like chocolate since there is chocolate. Btw it is actually sweet as well". Basically, I am trying to address a unconscious bias in their imagination of the taste. It also helps to understand better what they really like and what is totally unacceptable. For example, taste-wise, tomatoes are off limits to my older one ... for now because you never know when it changes. :) Hope this gives you some ideas.

"Tried that. Didn't work. He will literally vomit if anything touches his lips that he doesn't want to eat. Every time. So force feeding won't work."

Nobody suggested force feeding. Probably because it's a terrible idea.

You unceremoniously, and disinterestedly put food in front of them and when the meal is over, there's no more food available from any other source.

At 14yo it's too late for this, but for other readers, this will involve at most 1-3 days of annoyance and disruption. They'll be hungry and eat the food and you'll have quickly ripped off that band-aid instead of slowly, excruciatingly peeled it off bit by bit over the entire course of their childhood - which is a good metaphor for a lot of parenting.

This relates to one of the best pieces of parenting advice I ever heard: You almost never see a child throw a fit/tantrum about being put into a carseat. Why ? Because it has never worked. No matter what they do or say or scream, they know they're going in that carseat. If you see a fit/tantrum/stubbornness its because they know there's a chance you'll relent ...