Inclusion bodies almost never occus when you are NOT overexpressing a protein. Only way to get mixed inclusion bodies is by overexpressing 2 proteins simultaneously.
First of All I am appreciating to you for nice question?
I am not very much sure but I am giving one hypothesis why only one protein is going into inclusion bodies. I am agreeing with Dominique Liger comments. The second question I am asking why they form very stable structures. I am thinking that inclusion bodies form amyloid like structue because amyloid are very stable. Due to over expression chances of stacking with same protein is more. So I think it could be a possible reason.