With my webcomic character, who is Odd John-level smart, I solve the "cosmic rod" problem by not making her totally altruistic. Usually what involves her in trouble is her own curiosity and/or some consequence of some process she's testing and/or some technology stolen from her. (Again, like Olaf Stapledon's ODD JOHN.)
She has no particular desire to solve all the world's problems...anymore than you, if stuck on an island of just apes, would spend all your time making the apes' life better. That wouldn't mean that you have unkind feelings towards the apes, just that you have other things to do.
Reed Richards, Ted Knight, etc. should have discovered cures for cancers and AIDS by now, revolutionized the power grid and solved global warming with alternative fuels. In the process, whole areas of industry would have been thrown into chaos and society would have become unrecognizable and empathizing with people in it would have been harder.
Mindmistress (my character) has no such desire, and sensibly keeps her technology to herself...anymore than you would give a machine gun to an ape.