Big Daddy is in the roster because Irrational Games has an exclusive deal with Sony similar to what Activision has with Microsoft for Call of Duty. It's why all Irrational Game announcements are usually at Sony Conferences e.g. Sony'a E3 Presentation. It's also why the PS3 version of Bioshock Infinite includes the original Bioshock and supports Playstation Move, and is the reason their developing a Bioshock game for the Playstation Vita.
He's a justified addition, so please stop your complaining. He's an awesome charector.
A character from Bioshock Infinite would be justified, Big Daddy really isnt. He was picked for recognisability and nothing else, its a real shame because Elizabeth with her powers could have been a really cool character, and it would be an extra female.