So the cable pulls the payload across, to (lateral) orbital speed: this was my point about the payload bending the cable over.
1. The cable has to be strong enough to do this (which may be reasonable, given how strong it needs to be anyway - plus it's in tension)
2. The cable will still be bent over, by a force imparted at the payload. If the bottom is attached and the top is "fixed" in geostationary orbit, the force will move the payload laterally (lagging the orbit - west), looking like a kind of arrow, or "V" on its side. The force on the cable itself might be OK, as the force is in tension; and the curve of the bend might be gradual enough. (Or maybe it would end up straight, but tilted westward?)
It will also pull on both earth and satellite, slowing both.
Note that the tether only moves at orbital velocity at one point. Below that point, if you want to get into orbit, you must accelerate laterally after releasing the tether.