It's a bit more complex than you think. You need the right amount of sugar for the correct texture. Harold McGee (1990) clarifies this in his excellent book, The Curious Cook." He writes, "if the mix contains little sugar, most of the water freezes into large crystals...and the texture of the ice is hard and crumbly. If the original mix contains a lot of sugar...more syrup remains unfrozen, and the ice crystals are relatively small. The fruit ice ends up soft and smooth." His chapter on fruit ices breaks this down and explains it comprehensively. He identifies four types of ices, and provides tables for calculating the proportions of fruit juice, water, sugar, and (in many cases) a little lemon, for each. What he calls a "sweet water ice or fruit ice" is probably close to what you are calling a slush. It has enough sugar to remain soft in the freezer, but it is pretty intensely flavored. In this case you are looking at 30 - 35% sugar. The amount of sugar added depends on the type of fruit, thus the tables he provides. If that is too sweet, you can make what he calls a "medium sweet fruit ice", at about 20% sugar, but it will solidify in the freezer and you will need to allow it to thaw a bit to achieve an enjoyable texture.
The bottom line is that the amount of sugar is absolutely related to the final texture of your fruit ice.