What you got wrong is that, to harness energy from a moving magnetic field, you have to use something that doesn't move relative to it, a stator thingy.
But this I could be wrong about, if I'm not mistaken, when the field envelopes the conductor, especially in a vacuum, the most important part is not to keep things immobile but rather to assure that it does not have ability to begin to move in the same direction as the field. if an orbit was maintained, assuming it wasn't a orbit in the same direction as the field's rotation, electric would be produced.
besides, the sheer size of the inductor needed would probably make it collapse on itself.
In space? i doubt it would produce that much gravity, and I think that we can assume that the magnetic field wouldn't do it either; especially if we can assume (I guess here we take that leap) material tech more advanced than today.
Finally, producing electricity in space, whatever the means, isnt a good idea if you plan to use it for domestic use (unless you ALSO want to live in space,
I'm thinking giant massive colonies, not observational research stations, the first can do the second, but the second cannot really do the first.
Also, if in space, the ability to have a superconductor stable and inexpensive (temperature control) makes your electric go much much further than if on earth w/ our power line tech.
Is it easier to build gigantic coils in space with unknown consequences for the planet, or to just build a fusion reactor?
Well, seeing as both are theoretical, I suppose we can't actually tell

As for unknown effects, i still don't think it would cause statistical difference; between ions, and upper atmosphere movement, and all the rest that magnetic fields do with planets, some of that energy is already being consumed, just in the changing of direction and movement of 'stuff' ; on the other hand if the coils circled the planet entirely there may well be an effect, if we put it on the topside/underside of a ringworld like station/colony.
The field is between 10 to 14 times stronger than earths, so I have difficulty buying it would be consumed all that quickly in the millennial scale. Given human history is only about 3 thousand years old, i don't think we need concern ourselves on any scale much longer than that. If planned for 5,000 years longevity, it would probably last longer, assuming no disaster, and then the people are on their bloody own.