Such RC environments do exist today - most of deep-sea operation is conducted through remote-controlled devices, as is a lot of combat-zone flying. The Moon is close enough for remote-control (2.5 second feedback delay) and vacuum with robot with arms on wheels is a much more friendly environment than deep water with floating rig or a light airplane.
The Moon is even close enough for you to send another robot to kick stuff when the first one gets stuck.
Complex manufacturing will not happen on the Moon until there is some need for it, but having simple automated factories for cooking soil to grab volatiles (oxygen, water), to make rocket fuel (splitting water into LOx/LH2) and RC robots for digging construction sites and for assembling stuff sent from Earth would be very useful. If the volatile extraction facilities also make elements (tubular metal structures and sheets) for construction, all the better.
Having a stockpile of materials would be great when the time comes to establish permanent human occupation. It's not about removing humans from space exploration - remote control is severely limited by the speed of light and is not an option for anything beyond Moon orbit (although one could assemble space station components with robots before the structure is occupied by humans - that could remote control the robots from inside the habitat), but to make it easier to put humans on-scene later.
All of it seems quite doable and most of it has been done in the past. The Russians had a moon rover that was remote controlled from Earth.