Robin is hard to pull off so... Joker is Robin? You've said exactly zero things with this paragraph.
Only to highlight that for all intents of purposes, whatever Robin exists in the DCCU, it's equivalent to Thomas/Martha Wayne. We may see him, something happens, and the audience is left to see Bruce deal with it. Whatever this event is, will obviously be relevant to both BvS and SS given the minimal visual tie in of the Ha Ha Ha's. If it's nothing more then that, a traumatic event to help set the tone - and give a little bit of non-controversial backstory, then fine. I'll be a happy camper, but I think it'll be a missed story telling opportunity.
In a large sense, DC movies highlight consequences. Batman Begins/TDK hit this nail on the head w/ the escalation path to the joker, bringing down the mob, etc.
MOS plays on this nicely with what appeared to be a rather standard alien invasion/destruction scenario is actually a brilliant setup for BvS. Even after watching the trailer, we can go back and watch MoS and see action/consequence dynamics. (Pa Kent essentially commits suicide to protec the secret, Superman destroys the drone and clearly says things will be on his terms). Likely the consequence of that will be the opening act of BvS.
So that leaves Batman, whatever happened to Robin, and Batman's ultimate villian the Joker. Retelling the story akin to The Batman where Batman's first sidekick is Gordon's son, helps bring in the consequence of Gordon's actions (he bends the law a bit and enables Batman, his son/daughter look up and join Batman). Rather than a mysterious social commentary on Batman's actions like in TDK, we could get something direct -- you sign up to work w/ Batman, you risk getting in harms way and something bad happening.
Anyway, this is just a way to tighten up the plot lines and help push Batman into the Justice League, rather than what we often see - "I'm a part time member... i better get back to Gotham. I'm needed in Gotham." If we see Bruce peace out of something in JL because he's needed in Gotham, that'll be pretty weak.
So getting back to the Joker -- if you think about the Under the Red Hood animated movie. In it's climactic end, Jason Todd tries to force Batman to first answer why he won't kill the Joker, and then manipulate him into killing him. The answer he gives falls somewhat flat... "if i do that, I'll never come back." As if Batman letting harm happen to the Joker would immediately turn him into some blood-thirsty murderous villain-like vigilante.
i say, we want a heart-wrenching reason Batman won't kill the joker (or otherwise indirectly let him die a-la Ras in Batman Begins). One of the best reasons would be, deep down, he wants to save him/loves him/etc, and what better way to do that than to have Joker be once his side-kick, one of his few friends. No cops out "your one rule", no wish-washy Anakin scenario ("If i go to that dark side, my next step is to kill younglings).
so yeah, I think Joker was once Robin. I hope they tighten the plot and involve Gordon so we don't have extra Bat stuff hanging around Gotham to drag Bruce back there. And most of all, I want to see something new that we haven't seen before in comics/animated form. If we get Robin flashbacks, and a Red hood "ta da" moment with 0 build up, that'd be pretty lame - a handful of deus ex machinas to placate the fans, but we won't care.