Batman could have done more good as Bruce Wayne and instead dressed up like a bat to beat up street level thugs. If he was real, I don’t think it would make a difference what time period he was in, he’d still be traumatized by his parents death and decide to dress up like a bat to beat up street level thugs.
Instead of being trained by Ras Al gul, he’d have been trained under both 4chan and qanon. Instead of working out his emotional demons by maiming henchmen, he’d be an incel shitposting. Instead of Alfred admonishing him to be careful, he admonish Bruce to go outside and socialize once in a while