I never worried about "guaranteeing" that they ate. My child-rearing days are long behind me, but I used to simply say, "Fine, but don't come looking for snacks later."
Many times, it is simply an attention-getting gesture. Deny them the attention, and it probably won't happen often. Dismiss them from the table to their room to play alone. Next meal, they'll be hungry enough to eat.
No one ever died or got sick from missing a meal, but plenty of people have become ill after pigging out. (Assuming normal good health, and not some 'must eat on schedule' condition such as diabetes.)
Even when they were high-chair age--I never put up with fooling around and playing with the food. I'd remove them from their high chair and put them back in their play area, telling them, "If you just want to play with your food, you're obviously not hungry. Let me know when you're ready to eat; the food will be here." And then they'd get served the same thing that they'd been just playing with.
Today, neither of them are especially picky eaters as adults; my youngest will "eat anything," my eldest has followed my lead of being vegetarian...which still leaves plenty of choices to eat.