That's actually sort of been tried. See "Clara M. Davis and the wisdom of letting children choose their own diets" [1].
Briefly, Davis took a group of newly weaned infants in the 1930s and let them choose what and how much to eat from a set of 33 food items. The experiment was designed so that the caretakers would not influence the children's choices.
I don't think candy and soda were among the 33 items--I believe they were all reasonably nutritious foods but with very different mixes of nutrients. All the kids ended up choosing diets from among those items that fit well with their individual nutritional needs.
Briefly, Davis took a group of newly weaned infants in the 1930s and let them choose what and how much to eat from a set of 33 food items. The experiment was designed so that the caretakers would not influence the children's choices.
I don't think candy and soda were among the 33 items--I believe they were all reasonably nutritious foods but with very different mixes of nutrients. All the kids ended up choosing diets from among those items that fit well with their individual nutritional needs.
[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1626509/