I like to use braid because of the suppleness/line memory of the material when using hair rigs (I'm referring to leader material specifically, main line I don't think really matters and is more of a matter of personal choice IMO). I haven't really come across a situation where I felt the carp were line shy, but then again, like Curt, I use braided lines that usually blend with the bottom such as mossy green or brown. I probably wouldn't use those high-vis types like red, blue, etc. You can find carp leader-specific braids that are coated from online carp fishing stores but to be honest I do just fine using the 30 lb PowerPro from my main line.
You are right in that simple methods can absolutely catch carp; sometimes they are even preferable when surface fishing w/ bread or using mulberries. But I can't deny that my carp fishing greatly improved switching from simple sliding sinker rigs to method leads with pack bait and corn or fake corn on a hair.