My thoughts exactly from the beginning. If all the other characters he chose to use were at least their 'source' characters in name and identity, it'd be rather inconsistent and half-hearted to suddenly use a surrogate/proxy of a different name and origin for someone who is so major in other usages.
Making it 'work' is one thing...and certainly someone of Nolan's skill could make just about anything work. But his creative prerogative isn't to make anything and everything work, it's to focus on the parts that he feels work best for his version. He made it pretty clear from the beginning that he felt that Robin didn't fit that, and that his version of Batman didn't need him to be complete and satisfying. So there'd be even less reason to use 'part' of him.
And Blake as a young, idealistic and morally steadfast cop (and perhaps the mask-less, moral leader that Gotham's future needs) speaks much more to the ultimate direction of this storyline moreso than having to address the comic mythos. Had there never been a Dock Grayson/Robin in Batman's history, not still wold have been an appropriate choice.