Sublimation implies that the phase chance is ice > gas. Remember the PLSS originally had a boiler and then changed to a sublimator.
Yes, but that ice first has to freeze from the liquid phase. That releases heat of its own that must be rejected by some of the vapor leaving the sublimator. I suspect the overall effect is the same as simply boiling the liquid directly, i.e., heat of boiling = heat of sublimation - heat of fusion.
I wonder what factors drive the choice between a radiator and a boiler/sublimator. Off the top of my head boiling/sublimation being perhaps more efficient and lighter in the short term, but not so in the longer term. The Shuttle seems to have used a third variant of the process, a flash evaporator.
It's probably practicality. The porous-plate sublimator has a nifty self-regulating feature. When the ice forms, it blocks the supply of feed water. As it sublimates, it reopens those pores and allows fresh feedwater to flow and freeze.
Flash evaporation is how conventional air conditioning evaporators work. Because the coolant doesn't freeze, the flow probably has to be actively regulated to match the heat rejection rate. But it probably achieves greater cooling per unit size and mass than a sublimator, and that's probably why it was used on the shuttle where the heat rejection rates are pretty high.