No it wasn't. The point was to pass the symbol on. The symbol is not about everyone wearing a cape and cowl and fighting bad guys for a thousand years. If you think that's the point of the end, and the point of the symbol then you simply aren't able to look past the surface of the true meaning.
When Bruce said "Anybody could be batman" he's not on the nose about it, he's talking about what Batman stands for, anybody could stand up and fight for their city. Not everybody will but that's why Bruce decided to go to extreme measures so he can inspire people to fight for Gotham. It all traces back to the scene on the plane in Begins. Nolan even said in this version it was always supposed to be temporary, this Batman thing, he'll let go when he sees an opening for the people to be inspired by. Blake and the death of Batman by a nuclear blast is what tells Bruce it's time.
Blake can simply be anybody. Bruce doesn't know for sure that Blake will take the cowl, how could he? Things are left there for him in case. He knows Blake will carry the symbol and defend the city, but how? That's up to Blake. He could be a vigilante like Nightwing or Batman for a long time or only for a bit. They show the cave because there's tech that will be used, detective stuff for Blake to use if he doesn't want to use it as a cop (under the radar like Bruce).
Bruce couldn't predict that Blake was going to throw his badge in the river and walk away from his career. The cave is given to Robin as a gift "here, you do what you want with it, it's yours. You can use this tech with your police force to help catch the bad guys. Or use it secretely if you want to be a vigilante like me". That's the message.
Blake has a choice. That's why it's open to interpretation man.
Robin, Batman or none.
