For any person consuming a healthy balanced diet, how would distilled water flush electrolytes from their system? Their food would be providing them with plenty electrolytes, such as sodium, potassium, etc. Electrolyte supplements are unnecessary for all but more intense longer endurance exercise (same for energy bars). RO (reverse osmosis) water filtration systems are best in class - far better at removing contaminants than pitcher filters - some RO models have a calcium cartridge which is purely meant to improve taste, not save anyone from electrolyte flushing.
The usual cheap RO systems operate from household water pressure only. They fill a pressure tank at the output, allowing the purified water to be dispensed from a faucet. The pressure across the membrane is that input pressure minus the tank pressure. That's relatively low, so the efficiency is poor, wasting perhaps four gallons for every gallon of pure water.
You can improve the efficiency with an electric booster pump, or with a "permeate pump" that recovers energy from the exiting waste water, or by simply filling a pitcher with no pressure tank. I'd expect that even the most wasteful systems are still a small share of a typical household's total water consumption though, assuming they're used only for drinking and cooking water.
