I realize everyone's family does what works for them. But I wanted to pick up on a couple of reason posts.
One is the concept that gratitude is learned by limiting choice. I just wanted to say that my experience is different. When I was growing up my mother used food many, many times to "teach a lesson in gratitude" to the family. One time my father had wasted some money so we ate plain white rice for two weeks for every meal. Another time my sister said something rude about a meal and my mother fed her that meal for days.
What I learned in my teens and early 20s was first of all, that my thoughts, feelings, and experiences were not important at the family dinner table. I started to use my babysitting money to buy McDonalds after school every day (imagine what my arteries look like now) and I just tuned out at the table completely. When I got freedom to eat what I wanted, at university, I gained 30 lbs. For me, food = mother's control, and so later when food = freedom I exercised poor choices.
I realize that is an extreme example, but just think about what really creates gratitude. I think when people say "I learned to appreciate what we had" they are usually talking about a REALITY that their family had. When it is an artificially created lesson (no, you may not have anything else, even though the fridge is full and you can see that it is) I am not sure gratitude is what comes to mind.
Second, lots of people have talked about picky eaters - hating them, not creating them, etc. I wonder if you have read the research on this. While I do think there are some people who won't try things out of habit, scientific research does show that some people are "supertasters" or naturally picky. They taste and sense texture in a different way than the rest of us. After reading that and looking around my family, I honestly think that the vast majority of "pickiness" is either:
a) an inborn trait that you can fight all you like, but it will remain or
b) a developmental stage
Remember that between the ages of 2-5 in "the wild" children would be exposed to a lot of hazardous plants and so on. Their pickiness at an age when they are more mobile and capable is actually probably designed to protect them from eating poisonous things. Also, for most people in the world (and in history), foods were much more limited to what was available locally. Having so many different tastes may not be totally natural to a growing child, and enjoying the same food day after day (while adults tend to eat less, if their choices are limited) may also be a survival trait.
I am not saying anyone needs to be a short-order cook (I am not, although I'm willing to offer quick alternatives). I'm just saying that framing this as a MORAL issue with young children may be setting up conflicts that time itself would handle.