ViewNX is going to give basically the same output from a JPEG as the camera will - there are some slight differences, but they're close enough to be negligible for most uses.
The reason to show RAW+JPEG is so that you don't have to run through the post processing of converting to JPEG in the computer - either so you can give quick proofs to somebody else, or because you're lacking in time or available computing power; yet it still leaves you with a raw file for post processing later.
There are also a few times where the in-camera JPEG falls down, because the codec is more simplistic in-camera than the computer can and does use. One that immediately comes to mind is scenes with large chunks of sky alongside high detail areas end up with banding in the sky, and is especially bad with older bodies. By processing those images that the camera doesn't handle properly from the NEF, you can avoid that, while not having to process every single image you have.
Finally, there's the small help that if a card goes bad, you're more likely to be able to recover any given image since you have two chances at it. If the subject is important enough to be doing that though, just get a camera with two card slots: much easier in the long run.
The downsides, as you already know, is your already small buffer becomes positively tiny, you burn up storage space faster and so on. And the end if the day, for me, I carry around a powerful enough and portable enough computer to just shoot RAW, but there are uses for RAW+JPEG. I only used RAW+JPEG when I was starting to process the .NEFs and creating my workflow, to ensure I at least had a quickly usable image. Then, once I was settled, I turned off the JPEG and went to NEF only.