Like Batman, Superman etc. there is plenty of takes on Hal Jordan, all rooted in interpreting the original first Earthman recruited into the Corps premise, which is pretty fantastic, and always ripe for more.
Not only his role as the first human in the Corps and what he brings to that, but also what the experience brings to his humanity, the guy who is the first to come back from it, how he processes that, and then views and adapts(or not) to the Earth he once left behind, to travel the cosmos.
So long as good creative writers find the character more interesting than the other derivative versions, (sorry if that's harsh reality for you, but they do) , and have more interesting things to say about that character. I say let them have at it.
That said the franchise built right using the classic Corps premise can and has carried more than one book and character be it more humans or aliens, (except during the Kyle only era) so by all means do parallel books. John Stewart as the young artistic upstart, cosmic "architect", thinking-mans Green Lantern, prophesied to bring a new approach to harnessing and channeling will, was one of the more interesting concepts developed out of the franchise.
Not sure why that was dropped, (oh right to make Kyle that instead) and replaced John with the boring by the book military vet(even more derivative of Hal) version?
By all means somebody try and make John unique and interesting again.
But you'd have to give Kyle's young creative -going to change the nature of the power itself- arc, back to John, good luck.