Was the US not as susceptible to a decapitation strike?
In some ways yes, and in others no. Theoretically, it would be much faster for a Soviet boomer to sneak up on the American coastline and blot out Washington faster then the US could do so to Moscow in the USSR. At such short ranges, it takes ~5 minutes for a missile to reach from the Barents Sea to Moscow. It takes 1/5th that for one to go from the immediate American Eastern coastline to Washington. However, the US was much more flexible in inherently devolving launch authority because the US, quite simply, trusted their men. The Soviets didn't trust their personnel remotely as much so they had a much greater issue with devolving responsibility. In fact, there are persistent rumors that there are mechanisms in place that the Soviet/Russian leadership can remote launch ready-to-fire missiles in the event the personnel of a rocket unit disobeys orders to fire, so given such suspicions it would make sense they made devolving launch authority a much less flexible affair. Perimetr helped side-step this by introducing a machine that was incorporated into the decision making cycle as a decision maker itself, instead of merely collecting or distributing information for the decision makers. Machines don't have loyalties, they simply take inputs and turn them into outputs.
Perimetr devolves authority to those aforementioned mid-level officers only if triggered and Perimetr could only be triggered if four conditions were met: (1) it has been activated, (2) it has detected signs of a nuclear detonation on Soviet soil, (3) it has lost contact with the Soviet General Staff, and (4) contact remains lost for a certain amount of time (how much time is still not clear). If all criteria is fulfilled Perimetr then contacts the 3-5 officers, informs them that a probable nuclear detonation on Soviet soil has been detected, that contact has been lost with High Command, that therefore launch responsibility has devolved to them, and finally it requests permission to launch a retaliatory strike. If the officers reject the request, the system lapses back into it's pre-trigger state. If they approve, it broadcasts launch orders according to a pre-programmed strike plan.
The Soviets did consider cutting out the human element completely but... well, I'll just quote that quote from the wiki article up there...
"Now, the Soviets had once thought about creating a fully automatic system. Sort of a machine, a doomsday machine, that would launch without any human action at all. When they drew that blueprint up and looked at it, they thought, you know, this is absolutely crazy."