The other events you mentioned though are not "Civil War" - the basic premise of which is that all the heroes (or close to) split up, pick sides and go at it. These days, you also wouldn't have an event like "COIE" where Batman is so marginalized (look at "Final Crisis" - it shows how DC's priorities has shifted) Bats and Supes has been mentioned enough times in-universe that they're the pillars of the superhuman community, that it would be difficult for them to not have large roles.
I'd actually be more into a smaller version of CW that makes more sense and doesn't have to involve every single hero. Stories like "The Janus Directive" or "Rann/Thanagar War" were able to involve a large number of characters and steer clear of the Trinity in a way that was organic to the premise.