I can't quite say I've been completely successful yet with my 5yo, and I think younger kids might be easier than older kids, who have more opinions and ideas about their life.
My 5yo understands nothing more than that we are "eating healthy" because Pappa never ate healthy, and that why he has a big belly, and the big belly is going to make Pappa really sick. From when he was young I always just fed him what we ate, and while we were pretty CW, I did read about WAP when he was young, so we were a bit healthier than regular SAD, so I think that made the transition about easier.
My strategy is to increase the primal foods which he already likes, slowly cutting back on the non-primal foods, and slowly adding in new nutrient-dense foods. He always liked broccoli, orange vegetables, meat, cheese sticks, and salami. So I increased those foods - he takes cooked broccoli to school for lunch, he has orange vegetables for dinner, cheese sticks and Applegate farms salami as snacks. He still eats sprouted bread, Ezekiels 7-grain one, a lot of their other types has soy in it, and while sprouted soy down at the bottom of the ingredient list, he is a 5yo boy, so I avoid those. He used to love Nutella, but then we switched to peanut butter, then Smucker's Naturals, then Smucker's Organic, then Almond butter - he hasn't complained about the change. When I make popcorn now it's only about once a week, and I cook it on the stove with coconut oil and then drizzle a bunch of butter over it (I'm also ordering heirloom popcorn kernels through our co-op). We usually cook him bacon and eggs in the morning and have breakfast together. He wasn't a huge fan of eggs at first, and after his first bite of bacon he declared he didn't like it. But we just kept on serving it to him, and when he sat down to dinner last night (beef roast and carrots) he exclaimed "hey, where's my bacon!?" I put some small pieces of avocado on his taco salad the other night and he ate it without comment. So, progress, slowly.
In my experience kids are big fans of tender meats. Their baby molars have a hard time with anything tough or chewy, which is why they like hot dogs and chicken nuggets so much, the meat has already been broken up. I think cave people pre-chewed their kid's meat, but I'd rather use a food processor. I watch my kid eat dinner, and even when we were doing a standard 3-section plate he would always eat the meat first, the veggies second, and leave the potatoes/pasta. I always just shrugged when he did this, and now he is a happy little clam not having that stuff on his dinner plate. Baked sweet potatoes and sweet potatoes fries are his favorite "orange" options, so for kids who like carbs maybe you can add in a variety of different carbs and see if something takes. Who knows, some kids might fall in love with turnips, rutabaga, beets, or brussel sprouts. If they don't know they aren't "supposed" to like it, they might make it their new favorite food. If the plate is full of foods they like they won't really think of different options.
That being said, my kid isn't an angel. I took him with me to the grocery store the other day and he kept on running down the center aisles asking for chips, cookies, and donuts. I said no, no, no like a metronome. He also talks about McDonald's and Burger King a lot, especially the french fries. So if he is left to his own devices he'll stuff his face with junk. But at 5 years old he isn't expected to make wise decisions for himself. I'm leaving him at home when I go grocery shopping, and when I get home and he asks "Mommy, did you forget to buy Cheerios again?" I just say yes.
I also don't stress about him eating "birthday treats" at school. When I meet with his teacher I'll explain that we are keeping him very low sugar/grain for health reasons (we unexpectedly found that cutting out sugars and grains cured him of his nearly-chronic nosebleeds - seriously, he even got blood tests for leukemia and I got a reference for a doctor to cauterize the vein, but since cutting out sugar and all grains excepted sprouted there hasn't been a drip of blood). I'm not really feeling the need to send along an "alternative" for him to eat, but I just want to make sure he is eating only a small amount.
With the food commercials on kids TV these days it can be tough to make good choices for kids without them feeling "deprived." But honestly, even though 5yo asks for Trix yogurt because he likes the commercial for it, he doesn't actually like it very much. So for an older kid a conversation about advertising and making good choices for oneself might be a good idea.
These are just my ideas, but every kid is different, so you'll have to find out what works best for your family.