When the Human Race was made custodian of the Winslow, in exchange the Prime Mover guaranteed that the Human Race would not become extinct. The Law Machines are the main way he makes sure of that. They serve to curb the worst human instincts which might lead to self-destruction, the most likely form of extinction.
The reason the Law Machines were willing to allow the hacking of the election on New Hong Kong was because it was an interesting experiment, and it was only one planet. If the experiment failed, and all the humans on New Hong Kong had ended up dead, the human race would still be safe.
And it means that New Hong Kong is a "control". It's a place where The Law doesn't apply, so the Law Machines (and the Prime Mover) can see whether humans have advanced, matured, enough so that they no longer need to be kept on a tight leash.
Since the Prime Mover continues to guarantee the survival of the human race, the law machines will continue to patrol all human worlds (except for New Hong Kong) and enforce the law.
And that one lone Law Machine will continue to observe New Hong Kong, the experimental control. (And that's why, in the first episode of Gallimaufrey, he says that he serves a function and is content.)
- Aside from the speculation that the Prime Mover is the agency behind the Law Machines, that all hangs together and explains a lot. (The P.M. could have been the responsible party, if he sent 'em back in time as well; it's just that there are several other contenders who could just as easily be behind the arrival of the Law.)
