Batman had many reasons for not stopping Gotham's floating island from leaving, but the biggest was still the safety of the Bat-family.
The war between Darkseid and the Green Lantern Corps was destined to drag on for ages, with no clear victor. But Batman knew that Darkseid would not let him go. He had always been very interested in the half of the equation Batman possessed.
Earth was remote and weak, so there was no need to send an entire fleet. The best method was still to send assassins for kidnapping or murder. If they could not deal with Batman, then Gotham's floating island hanging above Earth would become the ideal target.
Hadn't Darkseid sent people over before? Though they had failed to kidnap anyone, it had served as a warning to Batman. This great monarch was no honorable man; home invasions and kidnappings were his specialty. Rather than wait, they might as well move the house away entirely.
After Gotham went to Hell, Batman felt somewhat relieved. But Hell was still not far enough. Someone like Constantine could come and go freely, and just as they had moved Robin last time, sending Gotham to take refuge in a more distant universe would be a good solution.
So he had tacitly allowed Gotham to head for an unfamiliar universe, never expecting that this universe was undergoing enormous upheaval. Gotham's arrival had surely changed the situation to some extent.
It was not strange that the lunatics from Arkham Asylum would go to New City. What was strange was that after all of them rushed into New City, there was no further word from any of them.
Batman keenly realized that they might have replaced their counterparts, and the most obvious example was Penguin.
Penguin was the mayor and had more opportunities