Froggie, to the contrary, the reason why real gedolim are hesitant to air their opinions in public are because there may be blind people who misinterpret their words free of all nuance. Additionally, the “Public Service” gedolim (the ones who literally give up their lives for klal yisroel) would not have as much influence or be able to do much good by involving themselves in sectarian politics.
You apparently assume that every ramification of every act of a Gadol is foreseen by said Gadol and/or that there is an alternative act that they could do to make the world a better place (because that is the only thing real gedolim think about).