So what do I do with my own picky-picky eater?
I keep the supply of 'preferred' foods at a low-subsistence level at best, and I provide the things that I wish she'd eat.
I also make pointed comments about dietary choices which are "healthy" or "unhealthy" (as opposed to good/bad).
I also try two or three different recipes of any particular food that seems healthy/worth cultivating as a choice, and
I am not a short-order chef. I make what I make, and I make it to meet the health needs of our household, and sometimes its preferences.
Not everyone here likes the same things, though, and I'm not going to avoid Dad's favorite foods just because DD won't eat them.