Just for the sake of argument...I don't have water filters. Never did. Well, my 2001 motorhome came with a under-the-kitchen-sink filter, but the first time I winterized my mh I had to remove it, installed the supplied "jumper"pipe...and never put the filter back.
Travel from NJ to Florida numerous times, and NJ to California 4 times. Sometimes the water tastes different, but never had problem with getting sick or any "deposits" (say from "hard" water or anything else) in the water system.
If filters give you peace of mind, go for it.
Just FWIW.