Most possible hero? Of course. He's totally plausable. The only way a Superhero would ever function in a Captialist society such as ours would be if he was at the pinnacle of that infrastructure.
Likely? Not at all. Rich people are scum (seriously, what rich person ISN'T greedy?). As if any of them would be strong enough to be Batman. They'd do it for shits and giggles then give up after a week when they break a nail in a fist fight with a 13 year old car theif.
Somebody could become Batman, Couldnt have a Batmobile though, in a big city, you'd get stuck in traffic jams all the time. The Pigs would wanna bang you up as well for being a vigilante and causing major property damage and such, also, how would you know when a particular crime is happening, apart from teetering on the edge of a building all night? LOL Also how could you explain your injuries at hospital? or in public, realistically Batman would have loads of Shrapnel in his chin from all the explosions he's been involved in.
I am actually writing a story about a guy who becomes like Batman....his life imitates him and he decides to be HIM. It takes place 100 years in the future. I posted it at Batman: Yesterday, Today and Beyond...because well, I work on that site....Here's a link if anyone wants to read the 1st two Chapters...I am working on the 3rd.
Batman could happen 1 way. So a close relative or friend dies in a robbery or just criminal vandalism. He dedicates his life to stop crime. He joins the army and learns many skills and gains all kinds of weapons and whatnot. He is military funded so he isn't breaking the law. He creates a Batsuit with the military's help. He is granted special status as a law enforcer but the cops don't know his identity nor do they really want the people to think he exists. So the military keeps it from them.