What is the strongest case for nuclear weapons?

I recently finished the Doomsday Machine by Daniel Ellsberg, which makes an extremely persuasive case against nuclear weapons (IMO). I've heard that some academics argue that nuclear weapons have been a good deterrent to great power conflict or that the US should spend billions to modernize its arsenal for command and control reasons. 

What are the strongest arguments/pieces of evidence for views like this? 

I basically think that the risk from accidental launch -> global thermonuclear war is high enough to offset a lot of great power deterrence, in expectation.