im sure the substrate affects the quality of the mushroom or we would all grow on sawdust.
Of course it does. But not in the way you think. There is a baseline of available nutrients to be able to grow.
So when people case, they choose the easiest best for their particular strain. Historically people thought about cow crap because that' where you find the mushrooms. But in many cases, the fungus was in the grass and the poop merely triggered some pinning. Coco coir has almost the same available amount of nutrients as crap, and is easier to get and deal with (at least to me).
Remember, fungus is not plants, and just becuase cow crap is the highest concentration of nutrient that people think abount, that's for plants. Fungus can make use of far more sources of food, and will produce enzymes on the fly depending on what type of food is in front of it.
But, all this depends on the species. The cubes like coir or crap, hell, they love it, and will pin easily in it.
But the pans? Nope. They will usually spawn into grain and coir, but will not pin or fruit. So you have to transition them into wood, ie, via sawdust and plugs. Then they will consume that wood and kick ass. They are also FAR stronger than the cubes.
So are the pans stronger because they live on wood? Who the fuck knows. But wood has a lot of energy and nutrients in it, if you can just produce the enzymes to digest it. And they can.
Which refers back to your sawdust statement.