Seems like she's something almost entirely different every time.
Pretty much the point of this series, yes. ^.^
You occasionally have to let them do something ridiculous once and awhile to make them valuable.
Eh, not really. I mean, if you put Batman or Green Arrow on the Justice League, yes, you're going to have to play them up a bit, though good writers can find ways to do that that don't involve Batgoddery. But there's no need or reason to ever bring that higher-tier world into their own street-level books. Gotham works just fine without Despero, or Sinestro, or Grodd.... or Cheetah.