Even when a large pot of pea soup has been made properly, if it sits for a while, as in a restaurant, the suspended particles will settle to the pot bottom, leaving you with an almost clear broth on top. All non-clear liquids have solids in them. When the solids are heavier that the water, they will slowly sink.
You won't have that problem at home as the soup is gently boiling, which keeps everything in motion. This make the mixture of water, and solids more homogeneous. The fats seperate and rise to the top as they are more buoyant than the water. The seperation natually occurs if the liquid stands still for sufficient time.
When a binder is added, it holds all of the ingredients in suspension in the liquid, and doesn't allow them to separate.
Also, if you happen to add too much water to your pea soup, the same separation will occur. Again, a binder becomes needed.
Finally, there are people who don't like their soup with a heavy peas-soup flavor. It can be too strong for some. In that case, a binder, and a little cream adds richness, and dilutes the flavor just enough to satisfy those people.
There is no "one perfect way" of making anything. I try to make the foods I prepare work for everyone at the table. I've even been known to make the same food in multiple ways so that each person has their favorite version of it. Most people say that that is ridiculous. I say that I'm giving my best for my guests, or family, even if it takes more work. It's just the way I do things. It's almost a compulsion for me to go the extra mile.
It's what drives me to keep improving my techniques, to try other flavors, other textures, other food types. And when I find something really good, I have to share it. It's just who I am.
Seeeeeya; Goodweed of the North