If you do it that way you end up with 50% municipal or well water in your cooling system. Many people choose to ignore that as an issue. IMO, if your water is hard enough to leave spots when you wash the car, then you don't want that hard water in your cooling system.
I think you are a little too over paranoid about the situation of putting tap water in the cooling system. One of the reasons you have coolant is to protect the system from rust and corrosion. In order to corrode a system, it has to be neglected where the coolant is non-effective from being too old or simply not enough in the system. If you take care of these problems and keep the system flushed with new coolant every year, you will not have a problem.
There's a difference when leaving tap water on a vehicles surface, than inside an engine with coolant protection.
Do you also recommend to wash your vehicle surface with distilled water?
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