SLBMs were actually just introduced around the time the Cuban missile crisis happened.
I don't think Russia is so much concerned that they would stop being threatening altogether but their rhetoric is that any attempt to diminish the impact of their nuclear deterrent is an act of aggression in itself. In effect they view this as a second arms race while there is mounting political tensions between the US and them and the US and rising powers in the east.
Well yeah, they were around back then but there weren't really enough to act as a strong enough deterrent.
I think its just more for the use of internal propaganda. Putin and co want to cement themselves as leaders and having a common enemy can distract /be blamed by the people from all of Russia's economic and social problems.