Most materials (including steel) have issues with extreme heat. Steel can suffer “invisible” damage, where it becomes structurally weak, but there’s little visual evidence.
In that case, a cable that visibly melts or breaks, can be better.
Elevators have all kinds of passive braking systems. They might get stuck, but they only fall in movies.
It has to do with the weight of the cables.
That article posited that spider silk was a solution, but this may be better.