Additive white gaussian noise is quite well studied and pretty easy to remove with processing. So even if those last few bits are "just noise", if that noise is well-behaved, on the whole image you still have more information.
There's also the effect of pixel well depth. I forget the exact interplay, but I believe this usually ends up being the limiting factor before ADC resolution.
You can remove white noise with oversampling, but you can't usually oversample unless you're shooting a still-life scene and can take multiple exposures.
Otherwise, you can't strongly delineate between actual scene artifacts and noise.
Regarding pixel well depth, I suppose we can have a sensor with greater pixel size and low pixel count, like a 3840 x 2160 sensor in a full-frame camcorder. Since this would be sold as a video-oriented camera, lack of higher resolution will be a problem problem than in a still-oriented camera.
There's also the effect of pixel well depth. I forget the exact interplay, but I believe this usually ends up being the limiting factor before ADC resolution.