Even if it is anchored to a geosynchronis satellite instead of the moon, the other end must be anchored to the earth. The forces on the “leash” as the earth rotates would be enough to prevent the satellite from remaining in orbit unless it were of extraordinary mass. Those forces would be caused by friction (drag), the earth’s rotation, and anti-centripetal forces. Variations in wind velocity as storms pass through would raise havoc with calculations of the drag forces, causing the satellite to whip back and forth.
Don’t fool with mother nature.
Every simulation I have seen for stuff like this make too many assumptions. The physical forces that need to be accounted for I am sure we a)Don’t know them all, b) the ones we do know we don’t understand them well enough to do this.