Actual words proposals at bottom of post, if you want to skip down over my responses to other posts.
Finicky can mean a lot of things. My mother is finicky about beer-- she drinks it only when she’s in Eastern Europe or Germany, and will eat only imported Russian caviar (she knows people who send it to her). She thinks (and I concur on this one) that mac and cheese from a box is awful, and only the stuff made from scratch is any good (and when my mother makes it, it’s brilliant). When a little kid is described as finicky, you get one image, but with an adult, you tend to think of someone like my mother, who is a bit of a snob.
I’m a supertaster, and I eat a really big variety of foods. I don’t like things spiced with anything that has capsicum in it, but I like things with lots of mild seasoning, and I like every vegetable on the planet except eggplant, okra and radishes. I’m a vegetarian because I don’t like the taste and texture of meat, but in the whole, I like a variety of textures.
Being a supertaster just means that there are some things you can taste that other people can’t, and most of them are bitter, and other flavors taste really strong to you, so you don’t need a lot of them to season food-- other people might want a tablespoon of something in a sauce, but a 1/2 teaspoon is enough for you.
As far as bitter goes, I love broccoli, for example, but only cooked: it’s too bitter raw, and I must put a little sugar in tea or coffee to balance out the bitterness.
I know adults who declare they don’t eat vegetables, as though it is something to be proud of, they eat meat, but mostly fried, or luncheon meats, they eat bread, and pastries, cookies, etc. The occasionally do eat vegetables as part of certain kinds of sauces, like pasta sauces, or in casseroles, or in soup.
Those are all foods you can usually coax a toddler into eating, and so they are comfort foods.
So essentially what these people eat a lot of are comfort foods, and don’t want to try anything new, because it won’t be a comfort food-- you need to have a history with a food for it to be a comfort food.
If you want to stick with Greek, you could call it “anasirexia,” or in Latin, “consolorexia,” or “solaciorexia.” It seems Classical Latin did use “orexia,” borrowed from Greek, so it’s fair game, I think for Latinate words. If you’re a purist, you could try “consolocupidio.”