Following up on my longer post above and also my response to the picture that didn't include Firestorm, just as Alex Ross doesn't tend to include Firestorm, he was the very first "new" character to join the JLA. IOW he was the first that wasn't already well known and highly experienced. It made him different from every member before him, who really had to prove themselves to be honored by an invitation to THE super-team, the most exclusive ever.
And IIRC Firestorm joined in the last 2 years or so of the original JLA's history. So he wasn't a member of the original/Satellite team for very long, he was added very late in the game (as was Zatanna), and he sort of broke the rule that a character had to be very established and very proven before they could be considered for membership.
It's not that surprising that once they'd done that the next step would be to split up the team that was the only Justice League team from 1960-1985 or so. Firestorm didn't fit the prior criteria for membership.
Of course there were other characters that were invited to join but either never answered (Phantom Stranger) or said "no, you jive turkey!" like the very stereotyped Black Lightning.
Before JL Detroit though it was VERY hard to become a member. And Firestorm kind of broke that rule. So I see why Alex Ross opts to include Phantom Stranger or "Shazam" or Metamorpho but not Firestorm. He's doing his best to display the classic lineup when he does that and he apparently doesn't feel Firestorm fit the bill.
And according to all we knew of the team before Firestorm joined, he really didn't.
I love the original team (which again is also the Satellite team) most of all because of nostalgia but also because I like that there's a team that only the best of the best can join. After JLA broke that rule, there never was a top team like that again. Being invited to join (with one of those fancily scripted invitations that came with each new member) meant a hero had made it to the big-time then.
After Satellite era, joining the JL/A was never a big deal again because anyone could do it.