Remember children need much more carb heavy food than an adult. Sugars and starches. That's because they are growing. Also small children have a very small gut and generally cannot handle high fiber foods and find them repellent. High fiber veg is more of an adult thing.
I offer meat but don't worry when it is often not taken up. I always make butter and animal fats (chicken skin, cooked meat fat etc.) available, and it gets eaten quite a lot. I find rice is an excellent filler, not being wheat based but still starchy. For whatever reason mine refuse to eat root veg cooked, only eating carrots raw. I was the same as a child.
I do offer good quality ice cream that has no HFCS or veg oil. When bread and pasta are demanded I let them have it, but I offer other stuff first. Eggs seems to be very popular, and filling up on eggs takes the pressure off the pasta, which I consider to be junk food.
I do not attempt to force me will on my children regarding food. When I have a preference I merely fail to buy what I don't want it and offer what I do want them to eat.