Well, the authorities did shove the Cheetah into Arkham. That ultimately led to a conflict between Diana and Gordon. Batman was involved, but he ended up having to mainly deal with the larger War of the Gods spillover.
While I don't think the shared universe being used this way should be a regular thing, there have been some nice stories involving it. I enjoyed Harley's and Ivy's stay in Metropolis, and their interactions with the Superman cast. Brubaker did a fun Catwoman story with Selina and Holly in Keystone City causing trouble, with Selina commenting that she didn't like Keystone, thinking it too weird, missing the normalcy and sanity of Gotham. :)