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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.
I definitely remember they had drugs to make them affectionate of and protectors of the Little Sisters. With things like concept art it's hard to know how early in the process it was. Big Daddy's could've been nothing more than "boss type enemy with old timey diving suit." They could've been concepting their origins and purpose as well. The "guns" the middle and left are holding could also look like a tool. It could be something that serves as both. The mech suit from Aliens comes to mind, which was essentially the equivalent of fighting a bear with a forklift lol. Or maybe something like the rail spike gun from Fallout is a better comparison.
It could also be that they planned on each Big Daddy being a little different, or at least more different types than there were. I just double checked the wiki and there were two in the first game: the Bouncer (the iconic one from the cover) and Rosie. Also, it's saying the original candidates for the Big Daddy program were criminals and dissidents. The idea that in the right wing dystopia of Rapture they'd force invalids into the Big Daddy program to make them "useful" isn't terribly far fetched.
Maybe it was scrapped because there weren't many spaces where wheelchair bound enemies made sense.