Blake wasn't intended to just stay in there as a detective. Bruce repeatedly advises him to "wear a mask" in the movie. Its clear he intends Blake to actually be Batman.
Blake knows that the whole Gotham City believes that Batman has sacrificed himself to save the City, Yes ?
Blake Knows that a statue of Batman has been placed in the Gotham City's Town Hall by the mayor.
So, why many people believe that Blake was going to be the new Batman, I believe that if Nolan wanted to show that Blake is indeed Gotham's new Batman, he would have shown a Batsuit coming out of the Batcave platform.
Batman telling Blake to wear a mask and handing him all the resources to Batcave means that he wants Blake to become a new vigilante (Nightwing ?)
I think that Nolan wanted the Bat legend to end with TDKR.