Former Navy nuclear operator here. We made lots of very pure water on my aircraft carrier. Distillation was only the first step of water purification for us. We could make 40,000 gallons of distilled water a day. That went into steam generators, washing aircraft, catapults and if any was left over, for drinking fountains and crew showers.
It wasn't pure, but it was pure enough to drink and clean aircraft. You wouldn't want to have really pure water for drinking; it would make you sick.
Next we had charging water day tanks. These were tanks of distilled water that we would heat to just below boiling for 72 hours. This would drive out any dissolved gasses or other volatile impurities. This would give you the equivalent of RO water. Finally, before that water was injected into the reactor plant, it would go through a deionizor vessel that was about the size of a minivan. That's RODI water...just on a larger scale.
Distilling water is very energy intensive. The latent heat of vaporization for water is huge. We would use a vacuum chamber to distill water because it took so much thermal energy to do it at atmospheric pressure (and we had the power of two nuclear reactors at our disposal).