Maybe if you need a lot of Sulphur. While Io is the densest moon, and has an Iron core, the easily accessible top layers are pretty much all forms of Sulphur.It is also the innermost of Jupiter's moons, so the radiation would be hellish.
Wouldn't it be better to have humans at a base on Callisto teleoperating robots on Europa?
Io as a mining resource:Pro: lots of sulphurCon:1) About as radioactive as the generator room at Chernobyl. *DURING* the meltdown.2) lots of Sulphur. Very very few materials like being covered in suphur-containing dust.3) From LEO, IO is 5 times further away than the moon. It is also 55% further than Pluto. (in the only measure that matters, Required Delta-v)4) The radiation!5) IO is embedded in a plasma torus that shares its orbit around Jupiter. Flying through it, or hanging around there for significant time, will lead to interesting contamination of all exposed surfaces.6) Did I mention the radiation?7) IO is *also* connected to Jupiter's magnetic field via a flux tube, that extends more-or-less north-south from IO to Jupiter. Other than playing havoc with radio, and concentrating radiation, this is harmless. Also, IO's environment is quite dangerously radioactive.
The beauty of life-mining (or grey goo assemblers) is that this isn't subject to single point of failure situations, but instead works on the basis of huge numbers of throwaway, self-replicating, components.