I think Cyborg got Justice League status because they understandably wanted the Justice League to be at least a little more diverse than it was in the 60s (which is exactly what Bruce Timm says led to the inclusion of John and Hawkgirl in the TV show) and he was the most viable option from a corporate perspective. For a minority character, John Stewart made the most sense and probably would have been chosen had this been done prior to 2005, but this was in the era where the company was heavily promoting Hal Jordan as their next big A-list property, with his movie supposedly cementing his status as the next big Iron Man-type breakout character the very same summer the New 52 was supposed to launch. Obviously, that's now how it wound up working out (RIP Green Lantern: The Animated Series...you were great while you lasted), but it's clear WB was banking on it.
After that you had Static who, while very popular, was licensed from the McDuffie estate and thus not fully owned. I recall this causing potential issues with reprints and the like should the license expire, so again, a no-go.
Cyborg, though, seemed great on paper. He fills a techno niche in the team, he has a cool visual and, most importantly, he was a major character on the highly popular Teen Titans TV show that was still in recent memory (and airing in reruns) when this was all happening. So I can see why he seemed like an attractive choice and ultimately got the promotion.