there is already synthetic rope with dramatically better tensile strength, and it's displacing wire rope in many applications
The article did mention the use of a dual layer anti-abrasian coating for durability.
Honestly though, why increase height and density still further? There are stupendous issues here with efficiency with regards to food, water, and HVAC - if nothing else. My personal view is that cities of the present are essentially anachronisms spawned from 20th century post-industrialism intertia: artifacts of outmoded labour markets, planning laws and now-quaint geospatial efficiencies.
As the cost of living in cities rises due to the shortage of land, the requirement for importing food and water, and the artificiality of maintaining a reasonable healthy lifestyle in high density urban environment, my bet is that, broadly speaking, emerging labour markets (our type of industry, for example) based on new technologies for communications and a reformed education system will cause a mass migration of professionals away from cities, back to a more sustainable, decentralized model. Sort of like the green banker-belt outside of London, but on a far larger scale.
In short, I believe that while the city will not disappear, its face will change .. and certainly not primarily through ever-taller buildings.