I wonder how the story would change with big daddies in wheelchairs. Would they have a different job? Is that guy retired? Maybe Sinclair would develop crazy prosthetics..
I don't know all the BioShock lore, but maybe that concept art was meant for a hypothetical version where they use disabled people as bid daddy's. (I don't remember where they canonically come from.)
From what I remember, Big Daddies are the repairman of Rapture. They go around fixing any leaks in the pipes and doing general maintenance and repairs. When the Little Sisters emerge, Big Daddies are repurposed to protect them. (IMO this is not a suitable job for a disabled person lol) I think they might have done some psycho drug thing to them in order to establish the relationship with the Little Sister but I don't remember.