I wonder: We have ski lifts that detach from the cable so that they can move at a different speed when loading than when transporting. It seems like a similar thing could be done with an elevator so that there is a continuously moving cable, but it detaches from the cable to stop at a floor, and then reattaches after loading. You could add traditional doors, and a safety mechanism that halts the cable if a door fault causes a potential collision.

Perhaps added costs of this system make it less desirable than just adding more elevator shafts.