I'm probably going to lose some karma for this...
I, too, could come with a half-dozen answers that would be "far superior" to what 100+ years of the finest minds in the industry could come up with. But in reality, I really, seriously doubt that my designs would hold up because there's a *reason* that things are done the way they are.
Mechanical engineering is a *very old* industry, and any radical, new design would have significant hurdles to pass before it could be accepted and used in a real scenario. The cost of failure is very high and there are real lives on the line.
My first thought was to use something like a caterpillar drive along the sides of the shaft, each of which would operate like a mini elevator for perhaps 10 floors. But, very quickly, I can see that this type of system would have many, many more moving parts and consequently many more points of failure.
So, I think it *might* be best to trust that 100+ years of experience are, in fact, at work, and that we should first understand that there is *real knowledge* at work before assuming that our half-baked and thoroughly unproven ideas hold any merit in reality.... ?