sure, you're depriving them, of....sugar.

It's kinda like depriving them of marijuana or wine. Relative innocuous drugs, all, I suppose, and in some families and cultures children have wine or smoke pot, but no child really needs that (or sugar). If you yourself have been addicted to sugar (or alcohol or pot, for that matter), it seems that your children have a higher, not lower, chance of similar addiction, so why not eliminate the substance and perhaps give them a better chance of not getting addicted? Children have no more shot at rebelling against the absence of sugar by overindulgence than they do reacting against the absence of wine by overindulging later.