To ensure optimum taste of your brewed cup. Distilled water also speeds up corrosion of heating elements, boiler walls, rubber washers etc, thus reducing their life span.
For a superior quality extraction of coffee solids, the brewing water should have these characteristics, as per standards determined by SCA - Specialty Coffee Association of America:
If interested in further reading on optimum water quality for brewing coffee, you can download SCA’s water standards handbook from here: