What a load of bullcrap. If we are so lucky as to get space settlement at all, existential risk will remain the same as it has always been. And who still thinks weaponized asteroids are a good idea when multi-hundred-megaton nuclear bombs were totally viable by the 1970s?

It's a great highlight of the massive uncertainty inherent in the estimates - change a few estimates and you go from "no life in our galaxy" to "no life in the observable universe", but I'm not so sure the bottleneck is the formation of complex life (we can do a lot of reasonably impressive synthetic biology in the laboratory now).

Why not interstellar travel? That sounds like something that'll turn out a lot harder than we hope.

The business case, if it exists at all, is very limited.
The requirement for space settlement, if any, will primarily be ideological (and this includes fear of a perceived threat of planetary collapse - although I consider it unlikely that Mars will survive intact if, say, the US and China fight a nuclear war).
I strongly believe in the ideological rationale, and feel that sufficient justification. Space settlement and subsequent human propagation across the galaxy in no less than ten million years is its own justification - and to hell with the Fermi Paradox! We'll figure out what it is after we fill up the galaxy, or die trying!

The hypothetical paranoia dream Shuttle Bomber doesn't have to stand alert. It just needs to pull off a first strike. NASA and Air Force had three pads between them. If you disguised a massive nuclear first strike as a series of commercial satellite launches and a fake Spacelab mission on orbit (think Soviet maristrivoika), you could, in paranoid dreams, deliver 400 nuclear warheads or more, depending on orbits chosen in an overwhelming strike. SIOP involved 3500 warheads, so that is a nifty fraction, especially if you add in inaccurate depressed trajectory SLBM.

It's paranoia, but believable paranoia.

A remarkable study by the Soviet mathematicians.

The Air Force requirement for a once-around abort did drive major Shuttle design decisions - the double-delta wing in particular. In addition to once-around reconnaissance missions, some have speculated that snatching a Soviet satellite may have been another major driver of the requirement.

Also note that the depicted scenario makes a lot more sense when you add the word "MIRV" (or maybe MARV).
A single MIRV masses somewhere under 200 kg - the US Navy W76 weighs 100 kg or so.
A single nuclear bomber shuttle mission could have at a stroke delivered 50-100 nuclear warheads to targets deep within the Soviet Union, with limited warning (note that Proton and N1 variants were proposed for the mission in the USSR), providing a potential first-strike capability against Soviet C&C and bomber bases. While in hindsight is is obvious that such a thing would be a ludicrous way of acquiring that capability... well, so is stuffing an N1 variant full for nuclear warheads.

My impression was that the GEO command post was designed for a Looking Glass mission; that is, to exercise nuclear command and control of nuclear forces in the aftermath of a nuclear exchange.

With maneuvering fuel, such a GEO command post might be hard to intercept with the primitive nuke tipped ASATs of the time (you might need a Proton launch to get a big ASAT up there with 70s tech), and would be quite survivable. I've seen a life support report referencing a HEO command post as a design reference mission.

I wouldn't call the Expanse dystopian.
Earth is rich and happy (sure, 20 billion of the 30 billion of us are on welfare - but unrewarding lives with reasonable-quality free housing, healthcare, and food in a post-automation society seems not-too-bad to me, although the TV series seems to paint a bleaker picture of Earth than the books).
Mars is rich and happy (very nationalistic too, but what do you expect?)
They're exploiting the Belt and pointing nukes at each other, but so were the Soviets and USA during the cold war, when the standard of living in both countries was Not Too Bad (i.e. no famine, mass death, etc, etc.).
The Belt is for the most part livable. Ganymede and Ceres appear to provide a reasonable quality of life for a substantial proportion of inhabitants. Even Detective Miller's home appears livable. Ganymede looks well-developed and prosperous (until war comes). Tycho station is rich and happy. Mormons get an interstellar ship. A chunk of the Belt (maybe half to 75%?) gets left out of this prosperity. It's happened throughout history.
The world of the Expanse is not-to-bad. Until the Solar System collapses into war.