Robin...

Some kind of misguided fanservice? One of the things that bugged me most of all about that reveal was that he said it'd be under his real name, and I was like, "Oh! Dick Grayson! He's Dick Grayson! Awesome!" And then he just goes, "Robin", and I thought, "Oh, so it's fanservice without actually making the reference."

It was just thrown in there for no good purpose (as you point out) and they didn't even do the lame little wink well. That whole sub-plot was bungled from beginning ("I just kinda 'know' you're Batman," "Oh, you got me. With no evidence or real conversation about it and barely knowing who you are, I will admit that I'm Batman.") to end ("My name...is Robin. Not Dick Grayson, some people might not get that reference. So, definitely Robin. Does that mean something to you, fans? No? Why not!?")

It was just a shout out, that’s all and it’s all we needed. And in a way Blake is kind of a Robin like character, sort of.

I hated it too. Christian Bale hates Robin and wouldn't be in an adaptation that has him.

Not go anywhere? Bruce left him the GPS coordinates of the Batcave. Clearly he was going to take over Batman's role as Gotham's protector. Maybe as Batman? Or Nightwing? I doubt he'd dress like Robin.

It was just a nod to the character.