Why would you want to continue the game? I mean really? What is there to do? Finish a small handfull of quests that you could've just saved before hand and done?
Well, yes, and being able to do them without having the final battle hanging over you. It can feel a bit silly putting the life-and-death endgame stuff on hold while you run off looking for star bottle caps (although this is an issue for most RPGs).
Then there's visiting every last location on the map, looking for dungeons to dive, beasties to kill, treasure to loot.
And beyond that, there's virtual LARPing, and self-created quests/challenges, and achievement-hunting, that sort of thing. I think the technical term for this sort of stuff is 'dikeing around'.
And it'd be nice to be able to dike around with Lanius' helmet and sword, too.
(To be clear, I don't want a Broken Steel-style DLC for NV, it would be all-but-impossible given the story they decided to tell anyway. Nonetheless, it should only take a smidgen of imagination to realise there are all sorts of reasons people want to keep playing beyond the end credits, and most of them boil down to "I really enjoy this game, am attatched to this character and want to keep playing." It is paying the game a compliment.)