Why does industrially produced tagliatelle come in nests?
When making egg pasta at home if it's not used right away it's common to flour slightly and wrap into nests to dry. This is a simple and effective way to do dry your pasta without it hanging over every cupboard door, door knob, your dog, etc. I suspect that manufacturers package this way for marketing reasons to make it feel more authentic. 

When I make pasta I generally dry it in batches by hanging for just long enough to not stick then I create nests on parchment paper until more dry. These are also easy to store and pop into a pot of not as much water as previously taught by everyone.