The explanation previous seems misleading, the rockets sent up to give codes for launch, humans still launched them. Presumably before satellites, redundant fiber networks, and robust national communications they wanted a fallback in case communications get disrupted.
So not a dead man's switch, just backup one way comms system.
It's probably worth considering a return to a fallback comms system. In the 1990s, telcos were the pinacle of reliability. Sure, AT&T had local issues from time to time, and that cascading failure incident [1] in 1990, but things were on a path towards even more reliability. Now, I expect a several hour, multistate outage of 911 about every other year. Nationwide single carrier cell phone outages aren't uncommon either.
I'm just going to assume a hostile first strike makes satellite comms difficult.
So not a dead man's switch, just backup one way comms system.