Humanity has come terrifyingly close to wiping out unfathomable numbers of people with nuclear weapons, some of which were due to errors in early-warning systems... Here are a few examples of just how close we've got to all-out nuclear war:

• September 1983, Soviet Union - An error in the Soviet early-warning system indicated incoming US nuclear ICBMs. A counter-attack was averted when the officer responsible for monitoring for incoming attacks correctly concluding that it was a computer error, narrowly averting all-out nuclear war between the Soviet Union and United States.
• November 1979, USA - A computer error at NORAD indicated an incoming full-scale Soviet nuclear attack. A program that simulated an incoming attack was mistakenly displayed on the live early-warning system, resulting in intercept aircraft being launched and nuclear bombers being about to take off just as the warning was identified as a false alarm. It's not known whether the crews manning US nuclear ICBM launch sites were notified of the alert.
• October 1962, Cuban Missile Crisis - Depth charges nearly resulted in a Soviet submarine launching a nuclear-tipped torpedo. Soviet submarines equipped with nuclear weapons were instructed to launch if the hull was breached by depth charges or surface fire, the launch was narrowly averted due to one of the officers on board refusing to give his consent to launch. Had the missile launched, it would likely have resulted in nuclear escalation due to the tensions between the US and the Soviet Union during the crisis.
• And many other close calls

Even taking into account nuclear power and lives potentially saved as a result of mutually assured destruction (how's that for irony), how close we've come to all-out nuclear war could make a good case against the invention of nuclear weapons.

That being said, in a world where nuclear weapons and international conflicts of interest do exist, nuclear weapons become necessary for states that are global powers if even a single state possesses them. However, such extensive proliferation of nuclear weapons isn't necessary - As Carl Sagan once said, "The nuclear arms race is like two sworn enemies standing waist deep in gasoline, one with three matches, the other with five."

One thing that is certain is that the effects of a nuclear attack are horrendous and devastating - For anyone who doubts that, I'd encourage you to watch the 1980s TV drama Threads - Wikipedia... And if that's not terrifying enough, consider just how close humanity has come to all-out nuclear war (and for added horror - imagine watching it during the cold war, knowing of at least some of the close calls).

If you ignore the context of history, it's easy to conclude that nuclear weapons should not have been invented - However, if you consider the invention of nuclear weapons in the context of history, then you realise that there's a good chance that the cold war would have turned hot in the absence of nuclear weapons.

Which leads to the ultimate question - What's worse... Many millions dying due to a cold war turned hot as the most likely outcome after WWII in a non-nuclear world, or hundreds of millions/billions dying due to a potential all-out nuclear war that may not even have been started intentionally? The only answer I do have is that we're remarkably lucky that neither of these outcomes came to pass.