I like how he gave the coordinates so he could become his own Batman. I dont think Blake would just take the cowl, I think he would have his own twist on it. It would just come out of nowhere. If Blake was in TDK, maybe. But having a second batman in the film just wouldnt work to be honest. I like Blake being the non masked Batman of Gotham; getting Gordon out of the hospital, linking up with the police down below, linking with Special forces, becoming the man with the knowledge of how things are in Gotham. I thought he played a fantastic role, and it built him as a character for the audience to accept that maybe, this guy could take the mantle of protector.
But also, I reckon Blake would move into the Wayne foundation orphanage too, so he can get to the cave easier.