After binging Caped Crusader last night, I must say I'm really really actively hoping that if Matt takes anything from that show over to the Batverse is 110% that take on the Bruce Wayne playboy persona. Bruce Timm and Hamish Linklater came up with an amazing way of showcasing it.
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Pattinson would 100% /kill/ a performance like this (obviously adapted to modern times) and it's extremely easy for me to imagine Rob's Bruce being exactly like this if he has to start going out in public and putting on that front. Rehearsing lines in front of the mirror, trying to perfect his charming playboy smile, researching as much as he can so he can blend into that world as best as possible and create that persona.
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Even Bruce Timm noticed the weird spiritual connection there.
I think it's set up pretty nicely in The Batman too. Beyond just the fact that Bruce should obviously be more involved with philantropy, if he had been using a playboy facade like this he probably would've discovered of the 44 Below a lot earlier and been able to research it himself without having to rely on Selina.
Also as much as I loved the emo Bruce take we saw in The Batman, I think it'd be an absolute shame to have an actor as versatile as Robert (who also happens to be a sex symbol) and not have him do the whole playboy shtick at some point, as I think there's a lot of interesting things he could do with it as an actor.