My husband and I did a "Protein Power" diet (a few times over the years, the first time was post-pregnancy after our 2nd baby).... It isn't JUST cutting out refined sugar, but that is a big part of it. Refined sugars are in just about anything you buy from the store unless it is a fresh vegetable or a protein it seems like.
We cut out carbs--which, the ones that come from refined foods (white breads, for example) just metabolically become sugar in the body. We restricted our carbs (all carbs, not just ones from refined foods though) to 30 every day. That still allowed enough for a healthy garden salad with red bell peppers, etc, some nuts, cheese, and dressing with every dinner meal. Breakfast was some variety of eggs. Lunch was something on light bread (6 carbs per slice) like tuna or egg salad or deli meat with lettuce or peanut butter, or whatever.
Yes, it was quite challenging to give the carbs/sugars up. However, after doing it for about 3 weeks, it got easier, and if we did "slip up" and indulge in something with refined sugars (a birthday party where we had a small slice of birthday cake at the celebration) it made both of us feel just AWFUL. Not guilty-awful.... physically awful. Like stomach ache awful.
I have friends who have done the paleo-diet, and by virtue of mom cooking that way, their kids have done it basically with them (though the kids weren't restricted at all when they were eating away from home where other foods were served/available), and they told me that after doing this for a while, that they went to a potluck at church and the kids (of course) "indulged" in the breads and a couple of cookies (not JUST cookies, mind you, but breads and casseroles, etc---we all know what types of foods are typically found at a potluck-- carbohydrate Central, right?). They said that after they got home ALL the kids were complaining about how they felt. So it isn't just a "mental" thing. The younger kids (5 and 8) really wouldn't have made any connection to eating what most people consider "normal" food and feeling miserable afterwards and the change from "their" normal diet--unless someone pointed it out to them. So there's some more anecdotal evidence for you. LOL
When I was following the low-carb (and adequate protein) plan, I really did feel like I had more energy all the time, too. It was just too difficult for me in the long run. I spent way too much of my life hyper-focused on what I could eat or not eat and how much, etc. (You don't STAY limiting to 30 carbs, after you get to where you want to be, you increase the carbs to around 60 grams/day and that is enough to make me start craving them all again and it is easier to just avoid them altogether than try to have a full carb sandwich, then no potato at dinner, etc).
Now I generally do the Alternate Day Diet, where I don't not eat ANYTHING. I eat whatever I want, in whatever quantity. But only every other day. The in-between days I restrict my calories--which by virtue of the number I limit to automatically means no sugar. So when I get my "free" day (every other day) I really don't feel good if I load up on sugars and junk--so I tend to eat a lot more healthy on those days as well.
And this plan sometimes is difficult the first few days as well--- but staying adequately hydrated goes a LONG WAY...