Staying thematic isn't optional. One of the reasons the game is so good currently is that nearly all the interactions between powers make logical sense and stay true to a common theme.
Part of it is calling it "Invert power". If you just called it "rotate power" I think people would feel less like it ought to do something to radials.
I'd still feel gypped if it did nothing to radials tho!
"Take solace in the fact that if I had the ability to kill one person I knew from the internet, it would be you."