I love all the debate about Superman/Batman Clark/Bruce psychosis and which is real and which is the disguise. These are all great points.
I've always seen it as Superman is who he really is and he has always had to hide as a disguise in Clark ie put on the glasses. At his core he is the farm boy/alien who grew up on earth and always struggled with weather or not to do the right thing which is saving people when he can because he would feel guilty if he didn't. When he goes to metropolis he acts bumbling and cowardly. Fainting whenever there is trouble or conflict so he can skip away and be himself to do the right thing which is take action. Face in full view to show who he really is and what he can do to help. No hiding. Clark is the mask. Hence the glasses.
Batman is the disguise. He wears a mask. He truly is Bruce Wayne the kid who is scarred for life at loosing his parents and decides he needs to create a persona, a symbol to eradicate injustice from the streets of Gotham so that no one will have to suffer as he did. He also pretends not to be angry and not to want to do something about it as Bruce but that is why he does what he does. It is because Bruce suffered, Batman takes action. So he is Bruce Wayne doing what Bruce Wayne wishes he could do but only able to under a mask.