I think banning foods is generally not a good idea. But one has to look at the whole picture.
However, I see posts from earlier this year about your daughter's virus, low hemoglobin and so on. And you seem to think that "cereal" is a balanced breakfast, so we're just discussing which cereal? I think your husband is way off about "just eat anything" - yes, maybe he ate sugary cereals, but was his diet full of other processed foods. I also think that suggesting that "extra sugar would actually be good for her" is way off (especially with a history of illness and low hemoglobin). What medical or nutritional info are you using to base that on?
Your child is not feeling well, she's not eating, and she's falling asleep early? She needs a lot more than sugar!
Have you seen the label on most cereals? There are 30-40 ingredients! And don't be misled by the "enriched flour" or added vitamins - those are just to replace a small portion of all the nutrients stripped out of the processed flour to begin with.
What proteins and healthy fats is your daughter eating as well, especially at breakfast and lunch (which fuel her for the most active part of her day)?
If you hadn't eaten in a while, the last thing you would want is bland food? I would think the hungry person would eat most anything. But it's important to offer a variety of flavors, textures, and nutrients.
Instead of Cheerios and Cocoa Puffs, how about oatmeal? Real, whole oats, which cook quickly. Add some cinnamon (not cinnamon-sugar) to give it a delicious flavor, and top with fruit and nuts. Add flax seeds or flax meal. How about whole grain pancakes with whole wheat flour, oatmeal, wheat germ or flax seeds, fruit, walnuts and more? Then put a little real maple syrup (which has some natural sugars but isn't a bit bottle of high fructose corn syrup) for a delicious treat? How about whole milk with a little Hershey's cocoa in it for a chocolate treat? How about a protein shake (but not one filled with chemicals)? I make a smoothie in my mini-blender every morning with a balanced protein supplement, fruit (I mix it up based on what's in season and I add in frozen fruits), yogurt, and water. There are a million ways to make something sweet and also healthy.
How about a side of scrambled eggs? You could add some cheddar cheese to that. Or make a fried egg and put it on an English muffin.
We did a lot of things as kids that weren't good ideas. The notion that "I turned out okay" doesn't fly, especially with kids have many more medical and food-related problems now than we did. Ask any elementary school teacher what she's facing in terms of health and energy in her students in 2016.
Please learn more about children's bodies and their nutritional needs. Take your husband in to see the pediatrician, and take a list of what your child ate for every meal that week. Discuss.