To initiate a launch against PRC, Russia would have had to fake being the President and the entourage including various military brass who would have been able to confirm the identity of the elected official.
Thus the nuclear launch codes served the same purpose as red mercury.
Submarines do not have a voice channel to the president, or to the military command. They receive coded signals that instruct them to take particular actions. Creating the appropriate coded signal is a fundamental part of the launch control chain.
Also if the president is killed, and the vice president and the head of the senate... eventually the question is "who has the codes" - if it was "something you are" then the first thing that an adversary would do is kill the are and then follow up as they pleased while the c&c system flailed.
All it really means is that we were taken in by a PR scam that had nothing to do with launch security, and everything to do with getting civilians off the backs of serious soldiers who considered themselves better qualified to make decisions than the politicians.
And all it cost to run was to have one of the president's minders carry around a satchel that the press were told had "launch codes" in it. I don't know if the presidents were in on the joke, or even the minders.