You are the 2nd person to bring up the flaw of space efficiency. It is a genuine technical critique, and I’m working on a followup article right now to address it.

For single buildings of relatively small size, it probably doesn’t work. It’s not true that the space tradeoff is one-for-one, because elevators have moving parts that are more expensive (the moving parts of the car are already paid for because they are multi-application). A double corkscrew would have very good throughput (continuous operation helps a lot) but corkscrews have a minimum viable size due to the arguments you made and elevators are smaller than that size for small buildings.

A corkscrew car ramp that services multiple connected buildings, on the other hand, would change that equation.