Sure. But then you have to spend way more energy on the "filtering" part. It typically makes a lot more sense in terms of energy usage to just take tap water

Sure. But then you have to spend way more energy on the "filtering" part. It typically makes a lot more sense in terms of energy usage to just take tap water and run it through a polishing step (deionization and/or reverse osmosis), than to take the comparatively "dirty" water coming out of your process (dirty but not toxic) and try to clean that up.