
Re: Any rope is the problem
Well, the next step up from that is what Star Trek euphemistically referred to as "turbolifts".
Once you replace the old Otis rope-and-counterweight system with a rail-based one (even if it's only a rack-and-pinion type rail drive rather than a maglev) it becomes possible to construct points and sidings by which lifts can be shunted and routed around each other. This would save on shaft space by allowing multiple lifts to occupy the same track while still having the possibility of passing each other by swapping rails at the points as needed.
Of course the downside of any rail-driven lift system is power consumption, because you now have to have an engine on the lift car itself driving the car against gravity. This is why the rope-and-counterweight system was invented in the first place - the counterweight means that the only force that has to be overcome is the inertia of the lift car, counterweight and rope - only the difference between the car and counterweight has to be hauled against gravity. (Note that Earth's gravity counts for quite a lot of power; it's the equivalent of going from 0 - 100 km/h in 2.8 seconds, continuously.)
With modern technology, however, the power consumption increase inherent in using a rack-and-pinion driven lift could be offset by using the same regenerative braking system used in electric cars. A lift could generate energy on the way down, by using its gravitational downward motion to charge a battery via its motor-generators. This energy can then be re-used for the upward trip; the entropic loss can easily be made up via a live rail and hot shoe system delivering extra power to the lift. I'd be interested to see what the difference in power use for such a system would be compared to the traditional rope-and-counterweight system. Any engineers care to comment?
With a system like this, there'd be no theoretical limit to the height of the shaft either, other than whatever structural compression limits might obtain on the materials used to construct the shaft and the building itself.