While it's twice the amount of water, the water is not as dirty (when you shower twice as long you may not be twice as dirty and may not be using twice the amount of shampoo).
Is that reasoning unrealistic? I don't know a first thing about water treatment.
For drinking water, we typically process relatively clean sources of water to begin with, not wastewater. It will vary by region. (I don't think anywhere actually starts with wastewater rather than some more convenient and clean local source, outside of fiction like "Dune.")
To take a local example I am familiar with — Seattle gets most of its drinking water from the Cedar River watershed (rainwater). It is a relatively pristine source. Wastewater, including shower output, is treated and released into Puget Sound[0] (the ocean). The only way that ocean water makes it back into the drinking supply is via ordinary evaporation and rain.
So the treatment required on the second quantity of water is exactly the same as on the first, and you get linearly increasing cost.
