Not just Batman, actually, in fact…
every single character that can be referenced for this stereotype/archetype is also a Big Softy. Show him a struggling young couple, a stray animal, an old but still feisty craftsman, or anything similar, and he’ll put his blood and bones on the line to help them.
Conan. Mad Max. Batman. The whole bunch of’em, all softies. The inability to see that characterizes a large number of role-players who continually want to play vicious bad-asses who are not Softies and then wonder why no one wants to play with them, or why they never quite feel like they get the character “right.”
It explains something I’d never really tried to voice about why Batman ‘works’ in the hands of some writers and doesn’t in the hands of others, but the relation to PCs in RPGs is also a good one.