I can see most sides of this argument and I'll sit on the fence -
My mum ate nothing but tomato sandwiches for 2 years as a child because she was so fussy. Eventually the GP told my granny to bide her time as eventually she would eat normal food.
I was a fussy eater as a child and I remember being terrified of going to friends' houses because I wanted to be polite and eat what I was given, but I was scared of what food would be offered. My worst childhood memories include not being allowed to leave the table until the food was eaten, however cold and horrible. One of my best childhood memories was a friend's mother quietly taking me to one side and asking what I would prefer to eat and making me a sandwich with no fuss.
My nieces are incredibly fussy - like Jack Sprat and his wife. There seems to be no common ground between them. Their diets are different from each other, different from the rest of the family and very unhealthy. They are now both quite over weight, as a lot of their food is junk food. Everywhere they go the hosts are given a list of what these girls will / won't eat.
I truly sympathise with fussy eaters as I remember how awful it was to be one myself. For me, the big turning point was learning to cook myself and seeing what went into the meals. Once I knew what I was eating, I felt very differently about food. I still feel nauseous if I smell egg in any shape or form, and my heart really goes out to anyone (child or adult) who feels like that about food.
However, I have had occasions where I've patiently explained to my nieces exactly what went into a delicious beef casserole, how I made it, what it tastes like etc and persuaded them to try just a tiny bit to see if they like it, only to have their parents swoop into the room, tell me they won't like that and ask for chicken nuggets instead. This really upsets me as I feel the parents are continuing to make life hard for themselves, the children and their hosts, when perhaps with some encouragement the children might learn to be more adventurous.
I am fortunate that my daughter is not a fussy eater and will try most foods. She knows that we don't force her to eat something against her wishes, but we don't make anything else instead.
Sorry to be so long winded, but in summary - I think it's awful for a fussy eater and their parents, but I do sometimes think people allow it to continue when a child may actually be willing to start experimenting, with lots of encouragement.