Although I've heard the same claim about fluoro being invisible, I don't think that entirely true in all water / light conditions. However in any case, a lighter tippet will
a) be limper and allow a small fly to drift more naturally
b) sink faster since it has less water resistance

That said, I only carry 5x fluoro which I use for almost all my nymph fishing and most of my dry fly fishing. I use larger mono for streamers and large dry flies and smaller mono for very small dry flie.