So the constant upwards force is providing enough tension to keep the cable in the realm of a rigid body approximation? I would have assumed the force applied to accelerate the payload would also deflect the tether and anchor backwards (in a miniscule amount) and would have built up over successive payloads.
Not arguing, just curious. It's been at least a decade since I've messed with orbital mechanics.
It does defect the anchor from pure vertical, but like a ball on a pendulum the vertical force from the anchor translates into a horizontal force.
EX: https://www.researchgate.net/publication/312934526/figure/do...
Of course if you really dig into things it’s more complicated, but the basic principle is very similar.
Station keeping may be used to dampen oscillations, but managing climbing rates works just as well.