I don't buy that "anyone" could be BATMAN at all. Not even close.
The amount of money, effort, time, motivation, and psychosis that would go into "being" Batman is too much for 97% of human characters. Even Terry McGuiness could not pull it off without Bruce's input and micromanaging. Bruce Wayne is the only guy for the job.
Dick Grayson could do it but strictly on his own terms. He's even better at it in a lot of ways, but he's not the same "Batman".