Tomo Nagura are used for finishing, we make an abrasive paste that can be more abrasive than the Honzan. But we are not always looking for that to be the case. Most of us work the slurry so it breaks down and becomes finer.
Compared to Tomo Nagura, Mikawa Shiro Nagura are coarse, and they will make an abrasive slurry that is coarser than any true Awasedo. We use the Nagura instead of different stones that are softer and coarser. Using a harder stone with very abrasive slurry will make the most accurate edge. It’s also easier and less expensive to have one hard stone and 4 smaller less expensive slurry stones that provide a wider range of cutting power.
Additionally, we consider the effects of having a mash-up of particles to work with; working with Tojidoro that is loaded with a variety of particle sizes and shapes is considered by many to be one of the keys to maximum edge refinement.
Another possibility is we might want to use Nagura to refresh and flatten the working surface of our Tennen Toishi. Using a natural stone for this task ensures that there will not be any synthetic particles to mess up a well done Kasumi finish.