I'm not particularly paranoid, but I do notice mineral buildup over time from tap water. In fact, my dishwasher may be end-of-life because of it.
(and of course, as others have said, bacteria, amoeba, disinfecting chemicals, minerals from the house's pipes... did I mention that I'm not paranoid? :) :) )
But YMMV -- if you're happy with reverse osmosis, go for it.