The problem with White Lantern is it plays into the least interesting part of Kyle's character these days. Him "struggling" with and mastering godlike power is certainly his most played out character arc at this point and the White Lantern thing seemed to be an appeasement for otherwise sidelining him. Heck, the most powerful dude around and the least useful half the time.
It also kind of hinges on and redefines Kyle by Johns' status quo (GL itself does not have to be as it predates Emotional Spectrum Power Rangers wars) which...wasn't even a good time for Kyle.