Secondly... continuous distillation doesn't necessarily require lots of energy, since a lot of it could be recycled with counterflow heat exchangers and heat pumps instead of plain heaters (i.e. hot output and hot waste are used to heat up input to close to the proper fraction boiling temp, and the output and waste are only slightly warmer than the input mix). It still needs energy input to deal with losses and entropy reduction from mix to separate fractions, but this is also true about using any sort of membrane-based separation.