I don't think they've made an open world Batman game which I'd describe as "good". The last three Batmens have been mediocre at best games due mostly to their terrible open worlds.
I couldn't disagree more. Even if I'm not in love with the open world, I do think there are certain aspects of it that are very well done. After replaying Asylum last year I'm not sure how I feel about it tbh. Freeflow and predator gameplay all feels so simple and barebones compared to the sequels. Traversing Asylum is also tedious since so much of it is done through vents and corridor after corridor. I still thought it was a great game but it definitely made me appreciate how well they evolved the series with Arkham City.