DC is not keeping Hal out of the League. From the moment Johns brought Hal back, Hal has been a regularly occurring member of the League, with him and John swapping out during McDuffie's brief run because Robinson wanted to use Hal & Ollie for his disastrous Cry for Justice series. During the New 52, Johns included Hal quite prominently and hilariously in the Origin, but had him leave because Vendetti wanted him to be in space as the leader of the Corps (and, at that point, Johns had been writing Hal continuously for many years and had probably run out of things to say with him). Even then, Johns made sure to bring Hal back for his big final story on Justice League, where he was again featured quite prominently. Hal & Bruce's relationship is one of the clearest of the entire run, with Bats starting off hating Hal because he was as a headstrong hot shot cranked up to 11 and respecting him as one of the most heroic members of the team by the end.
I don't know about the rest of you, but I'm kinda glad Hal was spared Bryan Hitch's dull as dishwater run, but your mileage may vary.
As for Snyder, I think he used Hal very well in Metal, but I understand why he wanted to use John because the character was still underdeveloped in the comics and allowed him to introduce the Ultraviolet Lantern mythos (which wouldn't have worked as well with Hal because guilt and regret aren't really his big hang ups).
Snyder isn't using Wally because King wanted to use him in Heroes in Crisis in order to torture fanboys
That said, Barry's persona has evolved much more into the more quippy Flash we saw on the cartoon (who was Wally, but also incorporated elements of Barry's backstory similar to how their Kyle was very much like Hal)
I also enjoy seeing Hal with his old JLA buddies, and I still get to see that. Hal's weird relationship with Superman was handled beautifully by Bendis in Man of Steel (in which Hal is still a member of the League). Bendis is also teaming Hal and Batman up in his Walmart stories. Williamson gave us a nice Hal/Barry story a little while ago. Hal & Ollie had a nice team-up in Green Arrow during its Hard Travelling Hero arc and Morrison's got an Ollie/Hal story coming up in The Green Lantern.
Sorry, but there's no grand conspiracy to keep Hal off the League because he's still there, just as John and Jessica are. Now that Kyle's free again, Snyder's confirmed that he'll be showing up, too.