As a species, it's insanity. We should be looking to denuclearize as much as possible. Instead, US-Russian relations haven't been this bad since the Cold War; now the Chinese, seeing the US gone crazy, want to be the/a superpower by 2049. That there were multiple occasions on which pure luck saved the world during systems breakdowns during the Cold War should remind us that there is no military solution to peace and the continuation of the human species as we know it.Why would they want a huge nuclear arsenal? As long as at least one other country has an arsenal big enough to inflict unacceptable damage, they're not useful.
I think one needs to consider the period the design came out of. Not in-universe(*), but in the real world. The idea for the ship came out of the mid-80's when we were thinking about what life in outer space might actually be like. If we do get out there, chances are that we won't find any aliens anywhere near us or on a comparable level, and it's going to be mostly empty, boring, and dangerous. That's a good thing (kinda). It means that we can safely spread out into space without fear of adversaries. And it should remind us how truly precious we all are in the profound nothingness beyond our thoughtless planet. In the face of all that, a Galaxy Class starship bringing life to lifelessness is, frankly, a blessing.A Galaxy is an awfully big ship. It's sort of a flaw - I wouldn't want to send 1000 people and such a huge ship on a risky mission. But TNG Enterprise was put at risk all the time.
(* Usually the fan argument in-universe is that the Galaxy Class came out of a period of peace, one that didn't have to think about baddies after Glasnost with the Klingons. But the period is actually chock full of war and conflict with the Talarians, Cardassians, Tzenkethi, Tholians, and maybe the Jarada and the Breen. Plus fear of things going sideways with the Klingons, and Elements know what the Romulans might surprise do.)