I wonder how that would have effected migration of humans across the planet, and how their various cultures adapted and formed. Some would see the Moon every day and night, others might only see part of the moon on the horizon. Others might only have distant stories of ancestors who saw the Moon and left it, or stories of the Moon leaving them. Others might forget about it entirely...
I imagine some cultures might resist moving away from where they could see the Moon. The omnipresent Moon might become a sort of god to those that lived under it, such that they would fear traveling so far away from it that it left. Maybe others would fear the perpetually darker nights.
This seems like it could be the premise of a science fiction story, perhaps similar to Asimov's Nightfall.
It would certainly be trivial to make a diagram of el/az of certain craters or mountain peaks referenced to earth magnetic north so as to make chronometers and such for determining longitude irrelevant. No need for precision chronometers would have some subsequent effects on the industrial revolution etc. Of course on the other side of the planet they'd need such "high tech" instruments as chronometers so in sci fi mode, the high tech far siders would likely end up conquering the near siders via higher technology.
A geostationary moon, if tidally locked to present the same face to the earth all the time, would certainly be a convenient termination point for a space elevator. So rather than a space elevator dumping you off in space, you'd be dropped off on the moon. Of course some genius will start transferring the earth's biosphere, oxygen, carbon, etc to the moon and just dumping it there to terraform it. Obviously (?) you can't just run a garden hose to the moon and suck on the moon end and expect a flow rate, although it is sci-fi so maybe if you pressurized the earth side up to something approximately ridiculous, you'd be able to squirt water across to the geosync moon. I would not want to be in charge of that project...
I imagine some cultures might resist moving away from where they could see the Moon. The omnipresent Moon might become a sort of god to those that lived under it, such that they would fear traveling so far away from it that it left. Maybe others would fear the perpetually darker nights.
This seems like it could be the premise of a science fiction story, perhaps similar to Asimov's Nightfall.