"Elements within the Soviet space industry convinced Leonid Brezhnev that the Shuttle was a single-orbit weapon that would be launched from Vandenberg Air Force Base, manoeuvre to avoid existing anti-ballistic missile sites, bomb Moscow in a first strike, and then land. Although the Soviet military was aware these claims were false, Brezhnev believed them and ordered a resumption of [satellite destroyer] testing along with a Shuttle of their own."
Nukes from LEO aren't impossible. They're just impossible to do better than the current triad. Any breakthrough in propulsion that would make a plane change easier or less visible confers the same advantages to an ICBM. There is a narrow window in which orbital nuking can outperform, and that's almost entirely taken care of--and exceeded, in stealth--by SLBMs.
Space-based missile defence is not what’s implied by weapons that are “already up” and thus “give a lot less warning in a first strike situation?”
From GEO, no. From LEO, still probably no.
There may be a bird positioned just right so a small deörbit burn pots Moscow quicker than an ICBM could. But the moment you start burning, you’re caught. (Same as an ICBM.) And unless you have a really obvious orbital configuration that bunches a bunch of birds in a way useful for practically nothing but such a strike, you only get one or two such “early” shots before a wall of ICBMs would have landed.
Nukes in space aren’t about nuking the ground from space. It’s about space area denial through EMP.