According to Daniel Ellsberg the US did implement a scheme where regional commanders could use nuclear weapons without explicit authority from the President:

"Walking out of the theater, Ellsberg turned to his friend, another nuclear denizen, and said, “That was a documentary.”"

I read once that UK submarine commanders had the authority to launch if they couldn't contact London and the BBC was no longer broadcasting.

Makes sense the idea that your entire war plan hinges on one guy is stupid.

In descriptions of the process it always amuses me that they talk about failure to receive Radio 4 being the test (perhaps of it also being broadcast on long wave)...

https://en.wikipedia.org/wiki/Letters_of_last_resort