One would argue that armageddon is triggered the moment any nuclear warheads are detonated. The dual capability of many launch vehicles keeps things ambiguous until something explodes, but make no mistake that nuclear retaliation would be imminent if not immediate. World leaders love being alive, but the chain of command trends towards an inevitable outcome. Strike before all your arrows are broken.

In my experience, a limited-destruction but full-scale launch would not be supported by leadership. We already have vehicles designed to fail, they are called penetration aids. Once terminal descent is achieved the fate of the target is sealed.

PALs and intentional weak links are the fail-safes. If a warhead makes it into orbit, the die is cast and we are committed to that scenario. If a warhead is detected by the target, luck alone might prevent a full-scale exchange. This has happened before, but it wasn't a missile launch that triggered it.

Tangential but relevant: Modern doctrine is not centered around population centers, although some are certainly included due to proximity or extreme tactical value. If you know why the Black Hills in NC would be targeted then you understand. Military forces with occupational capacity are concerned with counter-force, not counter-value.