I think the JL Origin arc just isn't a very good source material to adapt in other media. But you can tell that was basically how Johns wrote it, he knew that since it was the first arc of the New 52, it was going to be featured all over the place so he wrote it in a rather simplistic fashion: a group of heroes who don't get along fighting off an alien invasion.
Yeah, that was absolutely the intention. To give a modern version of the origin that outside media could adapt. As a result, all the characters were "turned up to 11", as Johns once said, so that everyone was easily distinguished from each other. I think it was successful in that regard, but I'd rather someone do a more long-form version of the JLA's early years that works as a comic book rather than a blueprint for a multi-media adaptation.
Cooke's New Frontier is still one of my favorite DC stories ever, but I'd like to see what happens next, after the team is already formed. I want to see young, wet behind the ears, rookies like Barry & Hal navigate working within a team with Superman, Batman & Wonder Woman, while J'Onn & Arthur deal with finally operating in open after being hidden for so long.
Add in Dinah right after she decided to assume her mother's mantle, and a young, swaggering Ollie into mix, that's a recipe for a potentially great story.
Yeah, Johns really dropped the ball by not really exploring that with all those personalities working together and becoming a team after the Darkseid invasion. Instead of jumping 5 years, the second arc should have introduced Martian Manhunter and been all about the JLA finding how to be a team, but that's me...
It's not really fair to Johns to blame him. He was given pretty clear marching orders from Didio. Give the New 52 Justice League an origin, then jump ahead to the present. His original idea wasn't even supposed to be an origin story. Flashpoint wasn't meant to be a reboot, just another continuity revamp. Johns & Lee were going to relaunch the Justice League comic as the already established team with Cyborg joining to help stop the latest invasion by Darkseid after being upgraded with a mother box.
The New 52 was a bit of an organizational disaster...to say the least.