Sugar in a frozen dessert is doing far more than sweetening. It determines how hard the finished product is, how smooth it feels and how quickly it melts on a spoon.
Dissolved sugar lowers the freezing point
Water containing dissolved substances freezes at a lower temperature than pure water, and the more that is dissolved, the further that point drops.
A sweet mixture therefore does not freeze solid at the temperature that would turn plain water to a block, and a portion of its water stays liquid.
That unfrozen fraction is what allows a frozen dessert to be scooped at all, since a fully frozen mixture would be as hard as ice.
Ice crystal size is what the tongue notices
Smoothness is not the absence of ice but the presence of crystals too small for the tongue to register individually.
Sugar limits crystal growth by keeping water dispersed among dissolved molecules, so crystals form in greater numbers and smaller sizes rather than a few large ones.
This is why a low-sugar frozen dessert made by an otherwise identical process tastes coarse, and why reducing sugar in such a recipe changes texture before it changes sweetness.
Churning and sugar solve different halves of the problem
Agitation during freezing breaks crystals as they form and works air into the mixture, and both effects contribute to a lighter, softer result.
Sugar controls how much ice exists to be broken, so churning without sufficient sugar still yields a hard product and sugar without churning still yields large crystals.
Frozen desserts made without churning compensate by increasing sugar, fat and milk solids, which is the underlying logic of a reduced-milk sweet such as kulfi.
Different sugars behave differently
The freezing point depends on the number of dissolved molecules rather than their weight, so sugars made of smaller molecules depress it more per spoonful.
Invert syrups and glucose therefore produce a softer set than an equal weight of table sugar, and confectioners use them to adjust hardness without changing perceived sweetness much.
This is why a recipe that specifies a particular syrup rarely tolerates a straight swap for granulated sugar without the texture shifting.
Fat and solids finish the structure
Milk fat coats crystals and interrupts their growth, and it also carries flavour compounds that would otherwise be muted by cold.
Milk solids and stabilisers bind free water so that less of it is available to freeze, which is why reduced-milk preparations set smoothly with no equipment at all.
The three levers of sugar, fat and solids are adjusted together, and altering one alone is what makes home versions of frozen desserts turn icy overnight.