Going by title alone, I would have to say Ascendance of a Bookworm. Myne is totally a menace. Doesn't fit the OP because she happens to show care and compassion about on the same level as the typical western raised person would feel, but every time she goes on an inventing tare she creates huge problems for everyone.
Unfortunately, her inventing stuff happens to also give her more influence in society, and the more influence she gets, the wider her reach becomes and the more people she sweeps up in the next disaster she pulls everyone along with her on.
(For anime only people who saw the way season 3 ended, just imagine how much of a disaster she's going to be with THAT much of an insane increase in her social power.)
