There is no problem with Batman joining the league, other than the opinion and misconception that Nolan's movie is too "realistic" to fit into the Justice League universe. Batman Begins is science fiction. What else do you call "memory cloth" gliding wings, roof-jumping cars, and a microwave weapon that can vaporize water in a wide area but magically not harm people standing right next to it? BB may be better at conveying an appearance of realism, but it's just an appearance. It's verisimilitude, not realism.
Batman being in the JL has been controversial with Batfans since the '60's. Nolan's movies are not even relevant to putting Batman in a JL movie or making his parcipitation logical
and vital.
You can hate the OMAC storyline, but take time to realize why the premise would appeal to DC:
1. Bats has launched a private satellite to keep track of the emerging metas of the DCU and has learned much about some of them. When he loses control of the satellite he hacks into it and gets access to files and programming he knows nothing about. He also learns that the OMACs are linked to whoever is now controlling the satellite.
It is logical that he would feel compelled to reach out to heroes he feels he has enough information on to get in contact with. It makes his participation in a group full of super-powered heroes organic and believable.
2. It's a good device to introduce WW, Flash, GL, AM and MM by showing their individual acts of heroism, and then are all attacked by the OMACs, and unlike lesser heroes, they all beat the 'bots.
3. Bat's greatest strengths (ignored in BB) come to the fore as he reaches the heroes and then brings them together, and then ultimately sussing out the true threat.
We've all seen the false rumors, but the initial rumor about the lineup and the OMAC's make sense to me and am happy about. I just can't believe no one's really thought about how the OMACs can help with the intro of the JL without needing to be scene-stealing secondary villains.