Historically, I think the answer is even scarier: the Dead Hand system presupposes that a centralized power is necessary to start nuclear war, the American system has been to delegate that power to regional and even theater-level military commanders (particularly in the bomber days, when sending orders to the Pacific theater was never going to work in the necessary timescale). It makes sense from a game theory perspective--if the commander-in-chief was literally the only person with strategic command authority, an assassination could render the entire country vulnerable to an unopposed first strike.

An airfield on the northern edge of Japan is close enough to Russian airspace that, at alert, the local airfield commander was going to have to make the call to sortie their bombers while the runways were still intact, and once deployed it wasn't unimaginable that a Dr. Strangelove-style scenario could go down.

It's been a few years, but I think this was mostly detailed in The Doomsday Machine by Daniel Ellsberg.