If you want to build one, sure.

For the general publing in places with escalators and elevators, most people seem satsified using them.

You can also get mobility devices which you install a track with a motorised carriage along a stair, usually with a seat and controls on the carriage.

There has been prototypes made for robotic applications that allows a robot to climb a staircase. The same technology could be used to loft a person.

Imagine an escalator inverted. As the stairs of the escalator interlace with the stationary stairs the platform you would be standing on would go up or down the stationary staircase in a smooth and level.

I'm sure there are many such devices that have been developed for this purpose.

Regarding the wheel and hook system you propose there may be a way of safely implementing your idea, I'm just not wanting to think very deeply about it at this time.

For it to be practical, it would need to work effortlessly. And the power source needed to drive it would have to be fairly large.

The hook and cable arrangement would be inherently unstable to the user and would tend to cause the user to tumble down the stairs. There are many ways of doing what you basically propose however.

The Segway could be outfitted with stair climbing capability for instance. You've seen the little wooden toy where turning the crank allows to blocks to sequentially pass by one another! Something similar could be used to climb stairways.