This! Exactly this!
It was a cute idea that might have been fun for a couple of stories, then it took over everything. It's a canon-hog! It's the same reason I don't particularly like Lex Luthor or Reverse Flash or the Joker. They take over every little thing they touch. Geez, let someone or something else be important for a while!
Honestly, I know I'm in the minority but I would have actually liked to have seen more of GL's rank-and-file baddies. Like his Earth-bound foes. But then, Johns kind of messed up the ones he did use. (Ahem: "Mr. Johns. The point of the Shark as a villain is that he's an evolved creature that still has a shark's predatory mindset. Not that he actually eats people. You'd have been better off making him an assassin or a stalker or a serial killer or, yes, even a sexual predator if you want to go full sleaze").