"The ratio in widths between the surface and GEO, McCarthy calculated, was a staggering 10 [to power of] 50. In other words, the space elevator was impossible with the best materials then available."

I believe this is wrong. Though it's right in that the cable does get beyond what is practical to build- in the order of more mass than thousands of Golden Gate bridges, but not planet size masses. For fun I'm still looking at trying to fiqure out a closer approximation. When using exclusively steel, the hardest part is the first 2000 km up.
Here a crude table which illustrates this:
Earth's diameter 12756.3
radius 6378.15 km Earth's circumference: 40,075 km
300 km above sea level circumference: 41,960 km (100 lbs weighs about 91 lbs)
600 km above sea level circumference: 43,845 km
900 km above sea level circumference: 45,730 km
1200 km : 47,615 km (100 lbs weighs about 70 lbs)
2400 km : 55,155 km (100 lbs weighs about 52.8 lbs)
3600 km : 62,694 km
4800 km : 70,234 km (1/3 of earth's gravity)
6000 km : 77,774 km (1/4 of earth's gravity)
[At 6378.15 km above sea level if a 100 lbs object were on a tall pole reaching to
the ground it's weigh from Earth's gravity would be 25 lbs & at this height it has
twice rotational spin speed as sea level- reducing it's weigh further. This reduction
is not included in these numbers, though circumference distance give idea of this speed.]
7200 km : 85,314 km (100 lbs weighs about 22 lbs)
8000 km : 90,340 km (100 lbs weighs about 19.68 lbs)
9000 km : 96,624 km (100 lbs weighs about 17.2 lbs)
10000 km : 102,907 km (100 lbs is about 15.17 lbs)
11000 km : 109,190 km
12000 km : 115,473 km (100 lbs is about 12 lbs)
13000 km : 121,756 km (100 lbs is about 10.8 lbs)
14000 km : 128,040 km (100 lbs is about 9.8 lbs)
15000 km : 134,322 km (100 lbs is about 8.9 lbs)
[The circular velocity of an object in a orbit 15,000 km above Earth is 4.318 km/sec.
Something on tall pole would have circular velocity at 15,000 km of 3.352 times Earth's
rotational spin: 1.58 km/sec. This is more than a 1/3 of the orbital speed.]
16000 km : 140,606 km (100 lbs is about 8.14 lbs)
18000 km : 153,172 km (100 lbs is about 6.85 lbs)
20000 km : 165,739 km (100 lbs is about 5.848 lbs)
[At 20,000 km the orbital velocity is 3.887 km/sec. On a pole the circular velocity is
1.954 km/sec- slightly more than 1/2 of the orbital velocity.]

I plan on showing what a space evalator will look like using steel and also using Kevlar plus steel. It will be impractical- but it's "fun".
Also:

"What made nanotubes of interest to scientists, and potential space elevator developers, was the strength of these materials. Scientists have calculated the theoretical strength of these objects to be as large as 300 gigapascals, nearly 100 times greater than steel and 15 times greater than graphite whiskers. A cable made either of pure nanotubes or a composite material that included nanotubes would be strong enough to support its own weight, eliminating the need to taper the cable."
Even with the non-existing "nanotubes" you would still need to taper the space elevator structure, though it certainly requires less tapering.
Now if they mean 100 times stonger per weigh than say 3 GPa steel, then a non-tapered "nanotube" could hold it's weight if around 2000 miles long (about 3200 km). If this is segment tapered it would be lighter and be able to lift more weight and thereby reducing the mass of the rest of 30,000 km length. Probably beyond 10,000 km the height there wouldn't be a need to taper "nanotube" material. Or if material was instead 1000 times stronger you could ignore the relatively small benefit from tapering.

"The mobility of the platform would also allow it to shift the ribbon itself to avoid satellites and debris."

This at best is problematical.
And as far as saying this elevator would cost 10 billion and the idea of it lower launch cost is pie in the sky speculation.