Just adding my two cents, grant you I just picked up Civ 5 last week and play on marathon pace, nukes are a very very far away concern, so I am simply going off the information from this post, and what other players have told me.
The first thing people told me when I picked up the game is Gandhi loves his nukes, and they felt that it wasn't realistic for him to get Nukes. My response to that is, if Gandhi 100% authentic to his real life persona he would get steam rolled ever game. He preached none violence, meaning he should build no units, and only focus on a culture victory, which then would make it easy with anyone who could field a decent army to take him out. By coding him to go for nukes, it allows him to play as a pacifist yet keep everyone in line as a AI.
Secondly that Nukes are overpowered. Now if you have looked into Civ Beyond Earth, the idea is that some kind of cataclysm happen roughly 25 years where you end Civ 5 campaign. Also this event was devastating enough to bring ever world power to its knees and was known as the great mistake. Also at the Pax Panel they suggested that was a "small" nuclear war that occurred in Asia.
Which makes me think that Nukes play a fundamental role in the begging story of Civ BE. If that is the case, then it would make sense for Nukes to be the end all in Civ 5. Also noting that the Nuclear War happen in Asia, I would assume the Gandhi had something to do with. I personally would like to believe, that even though you can create history how you see fit in Civ 5 it would be very hard to bridge the Story Lines. Yet everyone knows Gandhi is Nuke happy...............
So in short, are Nukes Overpower and should Gandhi have them? I guess we have to wait three more months to see what the great mistake is. If it Gandhi starting a small Nuclear War, then I see nothing wrong having them being OP in Civ 5 or Gandhi being one the first to hit the button.