Wofano Wotanto
Hero
There have been several variations on that theme over the years, some dating back into teh Silver Age. Both Batman and Green Arrow (who was once a complete Batman knock-off, complete with Arrowcar, Arrowcave, Arrowboat, etc.) spawned an international legion of imitators so you had (for ex) British Batman and GA, "African" (because that's not a whole diverse continent or anything) Batman and GA, Spanish batman and GA, etc., etc. They were all terrible national stereotypes that mostly just copied their inspiration's approach back in the Silver Age, but (at least with the Bat-imitators) some modern authors have tried to rehabilitate them into something a bit less awful. Beyond that, I can't tell you anything about Batman Inc. though.wasn't there a "Batman Inc." series that basically did this? Superior spiderman sorta did this as well, with Doc Oc (in the body of Spiderman) creating squadrons of spider henchmen to keep the city safe for him.
Bruce has also been portrayed as resorting to robots ("Bat-Sentries" IIRC) to help police Gotham in some stories (eg Kingdom Come), and there was a very tongue-in-cheek video game a while back where there were gangs of vigilantes dressedin unconvincing Batman costumes fighting in the streets with other gangs dressed like Joker.
The last I checked OMAC (the Jack Kirby creation) was also supposed to be Bruce's fault, with Wayne Indistries having secretly built the Brother Eye AI satellite to monitor the Earth for emergencies and if needed, turn unknowing civilians into super-powered OMAC emergency response drones with nanotech they'd been infected with without their consent or knowledge. If that sounds like a dystopian horror show that could easily go tragically awry, it was. Bruce is very dumb sometimes. As someone who quite liked the original OMAC I found that particular re-imagining especially offensive on many levels.