Well, I can't speak to who the best Batman in movie history since that's a subjective judgement , but , I agree, his Batman has received near universal praise.
The issue I have, is that his Batman, and more over , Reeves's world, doesn't fit into Gunn's vision of a DCU , very intentionally so .
If the concern is two Batman's at the same time, and audience confusion,
then wait for Reeves trilogy to end , then introduce the older,
Brave And The Bold version which has had several Robins, A Bat Family, etc.
Cater
that Batman to a world where Supergirl, The Lanterns, The Authority etc all exist, and give that Batman his own story that isn't bound to what Reeves is doing.
As far as someone new taking the Batman role for
Brave And The Bold : if the actor is good, General Audiences will except him.
I actually I'm part of the faction of fandom that Considers RDJ as Doctor Doom, totally lame , so , that example doesn't persuade me.
I understand how alot of fans would like Battinson to be the DCU Batman and for him to interact with other DC heroes.
But I prefer Reeves vision for
his Batman world remains: a world without Amazon's , Metahumans, Aliens, and Lanterns .
I prefer Battinson stays in that world where he takes on freaks, serial killers, mobsters, and corrupt officials and where he doesn't go to an outer space space station to interact with Metahumans and Aliens.
The idea that while Oz is out there trying to survive ala
Carlito's Way , in addition to his own interpersonal relationships , Darkseid or Mr. Mxyzptlk could be out there somewhere as well , just doesn't sit right with me.

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