I've taken a look into this for you. Next version will have a properly aligned local axis that's oriented with the object (Z normal for plane, Z along long-axis of cylinder, obviously not applicable to sphere).
However, turns out the maths for cube-fitting is really complex (more so than the shapes already covered), and possibly not doable in blender without relying on external dependancies (which I don't want to do).
I implemented a couple of algorithms for fitting cubes/cuboids and they were, to be frank, rubbish, and it'd be way quicker to just hand align a cube. I'll keep an eye out, but don't expect cube fitting anytime soon, sorry.
Shape Fitter
it's nice but.. please, add cube as an option for shape, and local/global orientation parameter...