Yes, I was not sture about this part for a minute - but the main thing is, that deep underwater nuclear detonations create significant pressure changes and with such scale plus water weight overhead - there will no materials able to stop flooding and hull tear, theoretically - and we are talking multi-megaton devices, which tend to generate a lot of energy, even if most of it escapes as gamma...
I also never said it was a single-compartment ship, just simply that if given enough time and effort, anything can be destroyed - for instance if most/all compartments get damaged - I just think somebody would have found a way with so many possibilities the assemblers give and it is hard if not impossible to protect against every single threat (that's why I'm also a bit scared for the future). Also - keep in mind that the ship was not yet complete (hmm, which part I may have missed in the description).
As for the logic and reason - at first I was going to describe a network of inter-connected undersea bases - but eventually went for a more "dramatic" approach - since it is not like it's a central point to the story or anything.

Besides - when was the last time anybody has seen a smart government? You know how the bureocracy works...

But I really do appreciate picking it up - it is the second least feasible thing that found its way into the intro, I believe ;)