If you can extract work from the field generated by the supercurrent, it must come from somewhere. Small supercurrents make small fields, so things like adiabatic CPUs seem interesting.
Can you extract work from a constant magnetic field? As I remember my physics education, constant magnetic fields don't do any work, since they apply a force perpendicular to the direction of motion.
I'm not a physicist, but I play with circuitry... two nearby loops of wire are magnetically coupled. If one is a superconductor with some stored current, and the other is a normal conductor with some resistance, then it stands to reason that the supercurrent will burn heat off in the resistive loop.
What happens in the scenario where the superconductor coil is just replaced with a permanent magnet? I'm pretty sure the energy that the loop dissipates comes from the energy required to move the loop into position, which the inductor experiences as a changing magnetic field.