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That's the neat thing about geostationary orbit. If the station at the upper end has enough mass, its own centrifugal force keeps it anchored in its orbit.
It's passed geostationary orbit. Geostationary orbit is balanced, but it needs centrifugal force pulling out. So, you need to be going faster than the orbit wants, hence, further out.
Except that you would drag it out of geostationary orbit every time you used it? Like no matter how heavy it is your still moving it closer every time you pull on the cable. You would need to constantly thrust equivalent to the mass of the cable and whatever the cable is pulling. At that point aren't you still basically just launching shit?
The more you think about it the dumber it gets. You would need to constantly move reaction mass to to the platform to create that thrust, but you'd have to use that thrust to counter the mass that you are bringing up. It's all the same problems as conventional rocketry.
Think of earth as a rotating bowling ball, with a string attached, and a tennis ball attached to the other end of the string. The craft you launch is an ant walking along the string.
Its legs push against the string, but that's nothing compared to the rotation of the bowling ball that keeps the string tight.
Technically, the ant's climbing will slow down the rotation of the bowling ball over time, but this won't have a noticeable effect for many millennia.
Right, except that a bowling ball weights about 6kg and a tennis ball weighs about sixty grams, so we would only need to build a platform that weighs 1% of the total mass of earth.
It needs to weigh enough that it counters the momentum/drag of the cable plus the net of whatever mass is going up. Keep in mind that cars going down add to that overall value while cars going up subtract. Also, the general opinion is for the station/anchor to be slightly above geosync so the net effect of the orbit on the station is to be pulling away from the earth (there is some wiggle room depending on how robust your earth anchor is and the mechanics of your tether with respect to tension vs. compression, but most models plan for a little net lift). In other words, you also attach to an anchor on the earth (which could just be a chunk of bedrock) to counteract that net force. Since the net force of the tether (not counting the earth tether) would be away from earth, any net loss of momentum would be regained from the earth's spin (which happens whenever we launch a rocket right now). You could also have a spool at either end to maintain the desired tension on the tether while accounting for slight elevation changes due to net momentum loss or gain. On top of all that, the space anchor mass isn't really dependent on the mass of the earth so much as it is on the net amount of mass being lifted or lowered to the earth and the amount of time you want to wait to return to it's desired orbital altitude. And finally, if the tether was severed only the part whose center of gravity was below geostationary orbit would actually fall to earth - the rest would leave orbit.
My point is that it was a bad analogy because that's exactly what it is.
How is it a bad analogy? You seem to be treating it like a scale model, which i don't think was the intention. Moreover, most of the effects map over fine.