Why do you shred cheese before adding it to a sauce?
You're right that the smaller pieces of cheese will melt faster than a whole block when added to a sauce.

The main advantage to shredding or grating cheese is that you create smaller pieces of uniform size, and often smaller than can be achieved just by crumbling (at least when working with harder cheeses).

The smaller the pieces the faster they melt, and if they're a consistent size/shape you don't have to investigate the sauce closely to find when the last, largest bit of cheese has been incorporated. This helps ensure the cheese will be evenly distributed throughout the sauce.