I actually totally think this is a great approach. As kids get older and can understand nutrition, I think mandating "nutritious" foods -- even if it requires a small incentive -- in the long run makes them more mindful, balanced eaters. I'm a fan of Satter as well, but I do think at some point you're actually doing your parental duty by saying, "You can't live your entire life avoiding the vegetables on the plate" (well, ok, technically you could, but it's a wickedly bad idea). It's vastly different from requiring a child to clean their plate of a food they abhor or using the withholding of treats as a punishment.
For your little one -- how old again? If under kindergarten age, I'd probably just stick with what works for now. Logic about nutrition isn't going to help. Include whatever non-processed foods s/he WILL eat with most meals, and maybe start to increase the proportion of those to the less desirable foodstuffs. My littler one is a much less balanced/adventurous eater than her big sister, but there's only so far I can go, especially since she's the kid who gets hangry and has endless meltdowns in that case, so there's got to be *something* she'll eat or we're all in for misery.