The problem...is that the cable system must be constructed from a material far stronger than anything known.
Nope, the problem with the so-called space elevator is that materials are beside the point. Each point on the Hindooo Rope Trick has a different orbital period, and don't argue with me about it, argue with Kepler. A 22 mile long rope would be a test bed, and within current materials science -- once it is discovered that it can't be deployed, or that once deployed it won't stay that way, some lucky taxpayers will be grateful they didn't pay for the entire boondoggle 1000 times longer. Anyone who votes for a space elevator better feel good about it, because it'll be last time they ever feel good about anything, if I'm alive to see them pull that ****.
The space elevator has always had fundamental physics challenges and always will.
The trans-linear vector theory is where the answer(s) lie. /s