Elevator brakes are one of the most elegant solutions known to man, and perhaps more crucial to the continued popularity of the cabled elevator. The brake is held open by spring tension generated by the interaction of the elevator and the cable. If the cable gets cut, the brake engages. That's it. Any other type of elevator would need a more complicated break system. Detection of fault conditions would be a separate action that triggers the brakes. That means delays, and the possibility of errors. It is practically impossible for a properly built cable elevator to plummet. You cannot say the same for any cableless concept design. One of the simplest ideas in legal liability is that if you opt to do something the more dangerous way, you're liable. You must have very good grounds to justify the risk.
You miss that in a pinion or cog driven elevator with the motors in the building, there is no need for emergency brakes - being stationary is the default state. Only if a motor moves the cart along will it actually move - up or down.
To me, that seems like far less risks than having a system where you need emergency brakes for safety, no matter how elegant.
And this system is in use in many assembly lines. The motors are stationary, and the carts won't move unless driven. And while most are horizontal systems, there are vertical ones too. Boxes with holes or pinions on the side are lifted or lowered by cogwheels, and there is no possibility of them falling. They can reach quite high speeds too, unlike the typical self-driven pinion-and-rack lifts that you see on boatyards and libraries.