I'm wondering if anyone else has noticed that coffee can have a distilled water taste and if they do anything about it.
Coffee cannot taste like distilled water. It's not possible.
I think what you mean is that the coffee in question tastes too clean or too dry. That can be caused by using filtered water with too low dissolved solids or water with too high sodium content. The best water to use for brewing is generally thought to be hard water rich in magnesium and calcium, with no chlorine and low sodium content. If the dry, flat taste of coffee bothers you, try using mineral water, or, if you really want to experiment, buy water additive made specifically for making brewing water like Third Wave (you can find it on Amazon). You mix this additive with distilled water to create mineral water. You can also make your own water additive with 0.75g epsom salt and 0.36g baking soda per gallon of distilled water.
Water quality is very likely the problem if coffee consistently tastes flat, dry, or "clean". The only way to test this is to try the same brew with different water.