You're right in that I don't see John's position in the Justice League as doing anything for him. When that Justice League movie bombed, I don't think DC/WB cared nearly as much for how the Justice League property would be handled, which is likely why John was allowed on the team. John being in the League hasn't done much for him from a story perspective, it hasn't led to any worthwhile multimedia appearances, or more action figures, and it hasn't led to his own title. Justice League did all of that for Cyborg (even though DC's attempts with Cyborg were ultimately flops), but I just don't see what it's done for John Stewart, unless you really, really like that idea of the Ultraviolet Lantern, and it's my understanding that hasn't even played a crucial role in a while.
I never considered it, but I'm not sure that John is in a better position now compared to Rebirth. At first, I thought this Justice League would clearly be a better place for John to be, but now that I've seen how things have unfolded, it's more difficult to say. I like the idea of John being away from Hal Jordan, because that paradigm wasn't doing him any favors, but at the same time, he's more or less doing the same type of thing now as he was doing then; just kind of being around and usually not mattering all that much. I would even go so far to say that he mattered more in Hal Jordan and the Green Lantern Corps than he does in Snyder's Justice League. I don't necessarily see his current situation as better, but kinda' just more of the same.