If they really wanted to do an earthbound GL show they could set it on Supergirl's Earth (I can never remember if it's 38 or 39) and his main mission could involve investigating crimes committed by (or to) that world's alien population.
My pet theory is that the reason Earth-38 has so many more aliens on it than Earth-1 is because there is no Green Lantern Corps in that universe. Think about it -- whenever we learn the origins of the alien-immigrant characters in
Supergirl, it usually turns out that they came to Earth because they were fleeing the conquest or destruction of their homeworlds. Maybe that's because there's no GLC to prevent all those conquests and destructions. In Earth-1's universe, where the GLC implicitly does exist (there have been references to a pilot named Hal Jordan and a disappearing Ferris Air test pilot), there are far fewer refugees in need of a new place to live, and maybe the GLC provides alien refugees with other worlds to resettle on, or maybe interdicts alien travel to Earth because of some Prime Directive sort of thing. Heck, maybe they even prevented Krypton-1's destruction, explaining the lack of Superpeople on Earth-1.
I'm hoping if they do go ahead with a GL show they break the Arrowverse Hero+Team template and have a smaller main cast, no elaborate Team Base standing sets, etc. One can pick up missions via ring just sitting in a pancake place, and if they really need to waste time faffing about they can do so sitting on a nearby park bench instead of "going back to the ship" or whatever.
Well, as I've been saying, standing sets are valuable for an FX-heavy show because they let you save money on sets and locations, so you have more to spend on FX and action. If the show is Earth-based, sure, the standing sets could just be things like GL's home and workplace and hangout, but if it's space-based, it's smart to have a ship as a regular location.
Also, in today's serialized times, large casts are kind of inevitable to generate story arcs. A more episodic, case-of-the-week procedural doesn't really seem like The CW's sort of thing. Although I gather that
Supernatural has generally had a main cast of only 2-4 people per season, so maybe it's not out of the question.