Are crystallographic omit maps only used with molecular replacement?
Experimental phasing and molecular replacement provide initial phases used to start model building. Later on (refinement, validation) phases are calculated from the model.

If the phases are what determine the final electron density irrespective of the amplitudes used

Both amplitudes and phases are used to determine the electron density.
If you calculate the phases omitting part of the model, the electron density in this place won't be biased by that part of the model. (It may be biased by the absence of the model in this place).