I think this is one of the problems comic books have that isn't often discussed, and uttering the phrase I used for this post title in a room full of nerds is apt to get some nice explosions of disbelief out of folks.
But the idea that billionaires can lead truly private lives is super, super old fashioned. It requires an era where reporters didn't delve into people's personal affairs and even if they did discover, say, that Babe Ruth was an alcoholic whore-monger, their sense of propriety (and the money to be made selling heroes) would lead reporters to keep it to themselves.
Batman is about as modern as Zorro.
Let's walk through a thought experiment to illustrate how out of touch an idea Batman is.
1. Bill Gates meets a young boy and takes a liking to him.
2. Bill Gates begins to spend a lot of time with this boy and is frequently seen with him around town at all hours, especially in the shady parts of town.
3. Bill Gates adopts this young lad, and cuts him into a sizeable part of his fortune.
4. Beginning to look into this weirdness, a reporter begins to hear rumors that Gates has been spending money unofficially. Like lots of money. He finds a trucker who reveals that Gates has been building some sort of underground dungeon, custom-made cars, various weapons, supercomputers, at the cost of a couple billion dollars.
5. Looking into the financial side of things, the reporter, who has now brought a financial expert in to help him investigate the case, discovers that Microsoft has secretly opened an entire new division doing research into things like exotic cars, aircraft, weapons and computers.
6. Delving deeper into Gates odd goings' on, reporters speak to a doctor off the record. This doctor has treated Gates and his young, adopted ward for various injuries, blunt force trauma, the occasional concussion, bruising consistent with multiple auto accidents thing like that.
The doctor was paid handsomely to keep his treatments off the books but finally had pangs of conscience after treating the young boy for a severe electrical burn and Gates for a gunshot wound.
7. After an outcry from shareholders about these odd expenditures and odd behavior, the SEC launches an investigation of Gates and Microsoft.
8. The young boy Gates been spending so much time with is found dead, beaten to death in one of the parts of town where he and Gates have been seen together.
I think we can all imagine where things would go from here.
The media shitstorm that would surround this would make the OJ case look like a press conference given by a minor league baseball team.