I'm a bit confused the ISS is only 408km from the earth's surface so why would it take 8 days at 200kph? Unless they are including the speed of orbit in which case the earth is already rotating at 1600 kph. What am I missing here?
The ISS will almost certainly be decommissioned by 2030 anyway, and we're not going to have a space elevator by then. There'll still be other stuff in LEO that we want to get to though.
Why the tether needs to be 36,000km long wasn't mentioned.
The ISS circles the Earth every 92 minutes. If we dropped a cable from the ISS (or another satellite at the same height), the anchoring point (e.g. something like a floating oil platform) would also have to circle the Earth roughly every 92 minutes. That's not feasible.
Satellites at 36,000km circle the Earth every 24 hours, which is the same speed that the Earth rotates. If the satellite is orbiting around the equator, going the same direction as the Earth's rotation, then we would not have to move the anchor (the Earth's rotation would do it for us)