Oliver mentioned Bruce Wayne, not Batman. Yes, Batman exists in the Arrowverse, because they have directly referenced him MANY times...on Earth-38. In all the years of Arrow, they've made no reference to there being another famous vigilante in another city on Earth-1, that I'm aware of, so the easiest conclusion to draw there is that Bruce Wayne simply is not Batman (yet) there. Oliver is basically his Earth's Batman (which would explain why he got Batman's villains and storylines). And that's why it would make so much more sense to put this show on Earth-38, imo, and just say Batman's out-of-commission for one reason or another, because in that universe, Superman's been around for 15 years and worked with Batman many times, so it's probably safe to say Batman's been active for well over a decade as well and might be due for a rest/retirement/injury or something. But they won't do that. Because they've never particularly cared about logic in this multiverse, lol. They'd rather set it on an Earth that has given us no reason to think there has ever been a Batman there, for...reasons.