Ah the way the pendulum swings.
Processed foods (like white flour) are easier to digest, but contain fewer nutrients, and by definition fewer "impurities"...be they bone/organ/fruitpulp/plant fibers/etc. They're easier to store/bake with/and don't go bad as quickly...which are 3 things that people have been struggling to achieve for generations. But since now, we're a wealthy society, we can afford to be choosy about what and how we eat...so we do.
Unfortunately, a lot of people are fairly uneducated about food and nutrition, so they jump on the latest bandwagon. Three of the latest crazes are "unprocessed", "no-sugar", "no-wheat". Lets hit these up one at a time.
1) Unprocessed
I personally prefer for MOST of my food to be the LEAST processed as possible when I buy it, but I'm also a young adult. For children and elders, it's frequently better for them to have more processed food in their diets...because it IS easier to digest and is less likely to transmit disease. When I say most, I mean it, there are some foods I will NOT touch, UNLESS they've been processed. Milk comes to mind. Remember the juice a few years ago that was making everyone sick? It hadn't been pasteurized, which is also a form of processing.
Processing BTW includes taking fresh organic fruit, boiling it (to kill bacteria, virus, & mold contamination), straining it and putting it in a jar of babyfood. Or if you do it yourself, into a bowl, or jarring it yourself. Cooking, cutting, bleaching, and separating out nutrients (like making your own chicken stock) are all forms of processing. Over all, the fresher a food is, the better it is for you. The less processed it is, the harder to digest...but the more nutrients. Not always the case, some foods CAN'T be eaten or the nutrients gotten from them unless they're cooked.
Processed foods last for a LONG time, so there's the length of time + the fact that you've already lost some of the more delicate vitamins/minerals/etc and that's before YOU'VE cooked it. They do however, last for a LONGER time. They're typically found frozen, jarred, or boxed. Crackers are a processed food...no matter what they're made of. So is wine. So is milk, unless you have your own cow. So is anything you eat at any restaurant. So is any meat that you don't plop down on your table raw with fur and feathers and entrails, or any fruit or vegetable that is washed or isn't the whole darn plant.
Certain unprocessed foods (like honey, Sugar in the Raw -my FAVORITEs-, etc) or anything that is unpasteurized, are more likely to contain diseases, and so shouldn't be given to babies at all.
Typically when people are talking about not eating processed foods, what they actually mean are things like french fries and bleached flours and canned anything. Processing is not evil. It just, like anything else, has some things that are inherent in it.
2) Sugar
So too, EVERYTHING contains forms of sugar. And it's a darn good thing. It's the only fuel that our body coverts to energy that our BRAIN uses. Fructose, glactose, lactose, sucrose, ... anything with an "ose" at the end of it designates a sugar. Tofu has it. Steak has it. Wheat has it. Even celery has it. Quite literally every food except for water has it. So don't buy into "no sugar in my diet". Buy into no PROCESSED sugar (sugar that is gained by crushing sugar cane, drying the juice until only the crystals are left, taking out the impurities -plant matter, & or molasses, why sugar in the raw is golden colored...it's just bits of the grass and molasses-, and grinding it) = white sugar. You can evaporate maple syrup and get maple sugar, pulverize fruit and get fructose, pulverize cacti, etc, etc, etc...but usually people are talking about white sugar cane sugar when they're talking processed sugar. If they're eating no "processed sugar" they're only getting their sugars from what plants and animals they eat; no maple syrup, raw sugar, etc. I've found that most people who say they don't eat processed sugar, actually do. It's just not white table sugar.
No Wheat
Some people ARE allergic to wheat and or gluten. My friends daughter died of a gluten allergy when she was 2. Very few people are actually allergic to it. More people have an intolerance. Way more people don't have the activity level that can use the amount of energy wheat gives us (children, by an large, DO have an activity level that uses up all that energy...but most Adults in America don't). People often say they feel like they have more energy when they quit eating wheat/gluten. That's largely due to the fact that they actually have LESS actual energy being converted from their foods...so they aren't overamped. Having too many calories (energies gained from food) leaves most people feeling lethargic. Think after thanksgiving. The body goes into a "store" mode. People who are REALLY active though, don't get that lethargy. So most people in this country (think non athletes, farmers, soldiers, children) tend to feel more alert and energized when they take excess carbohydrates out of their diet. Wheat products are the most pervasive quick calorie source in this country.
Like I said though, children (with the tremendous amount of energy they're expending growing coupled with a higher activity level) need a LOT more quick energy then adults. When they're taken off of their main source of quick energy...if they're not given another...they calm down, because they're too tired to be their usual bouncy selves. Sad in my opinion. But I shouldn't be surprised, some parents actually MEDICATE their children to keep them quiet. Kids aren't encouraged to play like we were when we were children, or having to work like when our grandparents were children. Parents seem to want quiet children these days. Well, starvation DOES work. So does zoning them out on meds. Obviously not my first or second picks.
Now, some people ARE allergic or intolerant of wheat and glucose. They have to go to a lot of work to synthesize their diet in such a way to GET the nutrients and energy the rest of us can do so cheaply and easily. It drives me a little nuts that people who have no intollerance, find that THEY do better with fewer calories, so they starve their kids.
So to, children also need a LOT more fats in their diets. It drives me crazy to see parents giving their infants and young children the same non-fat stuff they eat. Children are still growing their nervous system, which is made of MOSTLY fats.
Argh. In any event. This hasn't meant to come off as a rant. If you're really interested, and it sounds like you are...try taking some nutrition classes up at the local CC. Or at least go buy the textbooks and pour though.
As in all things, moderation tends to be key.
Good Luck!