I think some here are forgetting something.
Kids are their own people–for all the talk of blank slates and malleable characters etc, kids know themselves (to a certain extent). It is not all up to the adult in the scenario.
If you have a risk averse kid or one with high sensitivity taste buds or a combo of both, food can become a struggle. My oldest never had a food issue-she eats everything and will try anything. My second was reluctant to try stuff, but has expanded his horizons. He still will not eat anything with nuts in it or peanut butter (no allergy; he doesn’t like the texture or taste-but he will eat Nutella). My third child won’t eat sandwiches-which makes lunch problematic. He will eat the components of sandwiches, but not the actual sandwich.
Kids don’t automatically become picky at age 2, but that is when a bunch of things converge-independence, separation, and expanding food horizons. Makes for interesting meals at times.
Re the “bad parent”, lazy parent, weak willed parent thing-I think it’s an easy out. Sure, the OP’s example is of poor parenting, but they are an extreme example. Most parents muddle through, and most parents recognize transient willfulness vs a formidable opponent.
I was just such a child. Taste, texture, temperature, crunch factor, aftertaste–all were huge issues for me. There are still many fruits and veggies that literally make me gag. I think that the many, many nights of me sitting in front of stone cold okra has something to do with my distaste for it. Ditto plums, which my dad placed in my mouth*, and made me promptly vomit my entire dinner over the table. I never cried or carried on-still don’t-I simply refused to eat X. Very rarely, I would try X and find it palatable. This is true today. Perhaps my taste buds were shot off in the war, but a lot of food seems too spicey to me. Not as in hot, but too many “taste sensations” for this tongue. I have no doubt that some of the kids mentioned here have the same experience.
I am a big believer in vitamin supplements as an insurance policy. I would rather present the food, and move on, than make it an issue. My kids are older (8, 14 and 17), but when they were little, I did the same. They all eat a more varied diet than I do.
*he didn’t force it into my mouth. Looking back, they were frustrated and angry at my perversness (ity?). They are very controlling people, but were stymied by this. I say this from a retrospective viewpoint-it never occurred to me then.