Otis considered ropeless elevators, but in 1997 it looked like it would increase the energy consumption by 7X. Without counterweights, the motors have to do a lot more work. But maybe Multi can recover some of the energy via regeneration.
There are automated parking garages that can move cars sideways.[2] Those go back to the 1960s, and tend to be high-maintenance.
The Multi system looks really complicated mechanically. All those moving parts. Worse, they're on vertical surfaces in the shafts, where maintenance will be difficult. With regular elevators, the high-maintenance items are in the machine room. This will probably go into some prestige tower, but not be replicated much.
[1] http://www.barkermohandas.com/images/Integrated%20Vertical%2...