The main issue is making an effective and affordable system that works for all homes, since building codes need to be followed. It is absolutely possible to do what you mentioned, but it depends on what soap you use, how dirty you were when you showered, how much money and time you’re willing to put into the filtration process, etc. This many variables makes it nearly impossible to make a system that can be certified as safe, inspected, etc.
If you had a brain and no building codes, you could do it pretty easily, but building codes need to account for people who aren’t smart or capable.
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