I always thought of it as Robotnik actually is unable to run the planet on his own, and to keep All his factories pumping he can't spare the work force.
But the Freedom Fighters are a localized cell of Guerilla fighters, I am sure it can be done.
My idea is that it's similar to hypnotism. When you try to get a person who in a hypnotized state to do something against their moral code they always fight back. When Robotnik pushes them into using more "stressful" sub-routines like those of security and invasion it leaves the Robian open to rerealizing his humanity. For example, Chuck when forced into hostility by his programming lead him to be easily coaxed out of his mental enslavement (that and Sonic shocking him back to reality in a sense). One theroy proposed by Chuck in EoT us that the Ferrite-Field does not effect all organic tissue in your body. That sizable amounts of the nervous system remains engrained in the circutry like that of prefrontal synapsus are left for higher functioning and nueroplasticity while the lower brain stem is further engrained in the machinary, hence why the programming effects the will though not their awarness. Robians that have been shocked actually swear that they can even feel pain still. Since nuerons need nutrients it could also why Chuck "ate" that Chilidog once, but that is stretching it. I think Robians still have needs, hence why there is still so much industry. Robotnik's odd economy of resources is not self-sustainable in the least and niether are Robians. In Eot they need "Violet Vile" (the stuff in Chemical Plant zone) to survive. Violet Vile is a liquid refrigrant and anti-freeze that keeps important mechanisms from overheating, especiall while overclocked for certain procedures. Violet Vile is actually a contested resource in the Casino Zone as a needed resource for Robians and a recreational drug to Mobians, and one episode deals with the stuff in extensive detail. They also need lubricants like motor oil. Repair parts. And ocassional "vitapacks", an invasive procedure that hook into the remaining nerves engrained in the "nuerocircutry."
The use of Robians as a terror weapon is explored as well. But I will leave that for you guys to read on your own.