Importance of Crystallization Rate
The freezing curve predicts the amount of ice at any given temperature, which is a function of freezing point depression and hence the number of solutes (concentration of sugar, etc.). It doesn't predict anything about ice crystal size. What predicts ice crystal size is the rate of freezing - the faster the rate - the more nucleation is promoted, and the greater number of crystals of smaller size that will result. This is very important in terms of ice cream structure.