I see your point bright sparks and even agree with some of it but I think picky eaters are a product of many different things and it will vary from child to child. I grew up with a sahd and he only cooked one thing for meals and if we didn't eat it there was nothing else. I am a picky eater to this day despite that. I did and still do choose to go hungry vs eating something I don't like. I also have issues with some food and their textures so I understand when children have these issues too.
There are times that children need to follow instruction but I don't think a child should be forced to eat something they truly don't like. I know that children need to eat something at least 10x before their taste buds will truly know if they like it or not and I do encourage my dck's to eat their meal. Dessert around here is usually fruit so they do get that but if it's a special treat like a cookie, they need to eat almost all of their meal to get something like that. I don't like meals to be a stressful time(I feel that opens children up to eating disorders and food issues) and if a child doesn't eat what I cook than yes, they do probably go away hungry as they are likely only eating the fruit and a few bites of the main meal. I do not cook different meals for the kids as I just don't have the time. If it came down to a child NEVER eating what I cooked than yes, I would ask the parents to supply the food. Thankfully, most of my dck's eat what I cook and they all know they have to at least try it before I will allow them to not eat it. I always give it to them even if I know they don't like though because I do feel that they need to try it every time.
You are assuming picky eaters are not eating healthy food by the sounds of your post. This isn't always the case though.