No, because Batman isn't a real person with real constraints.
Sure, I mean, if you have a $1B, then you get to have a lab with gadget people making cool shit and you can buy a fighter jet and a personal submarine and you have the detective agency too.
But you don't get the rogues gallery of super villains. You don't get new knees every week. You don't get to save your local city, because the problems are mostly the problems that the people cause themselves. And solving all those problems makes you a tyrant, not a hero. And even then, the problems are the same we've had since before history.
This is why in the real world, we have philanthropy mostly aimed at education and the alleviation of extreme poverty and diseases as the main outlets for the billionaires. Because it's the only thing we think that works at all.
I guess, if you really wanted to be Batman, you could fund yet another study that would state how best to give away dollars. But, without even having to look, I know that there are a few dozen of them out there already and they all pretty much say the same thing: that it's muddy and hard to discern, but maybe if you squint, education and making sure people have food and shelter.
To be Batman, you already can do it. It's mosquito nets for the poor, it's giving that bum a $100 and an hour, it's volunteering with prisoners to get them to read, it's making sure your kids' classmates have a snack before the test, etc.
So yeah, the real world Batman is a boring stressed-out Mom that's active in the PTA, her church/community-center, and local politics. Real World Bruce Wayne is Steve Rogers before the serum.
I find GiveWells approach the most satisfying when I ask myself “how can I make my charity go the furthest”. https://www.givewell.org/ I also highly recommend Famine, Affluence, and Morality by Peter Singer, it’s a perspective changing book. Also, great comment!
