That raises a point I have been wanting to make. Did Bruce really fake his death or he just not confirm he is alive? Maybe just a minor difference but a difference still.
He did not create an elaborate fake death scenerio. It not clear how he would have died. It just assumed he did in the chaos in Gotham.
Obviously he did create a will. But he did not know what would happen to him. He really could have died. Also all of the people closest to him know he lived. Alred, Gordon, Fox, and Selina. He made sure they had clues or out right proof of his survival. Robin may or may not have suspicions.
So its really the public who thinks Bruce Wayne is dead. Everything in his will he wanted to happen whether he died or not.
There is no reason he could not show up alive someday if he ever decides too.