I'd just wonder where he was when her mom was getting drunk and leaving her to fend for herself . . .

Plus, her reactions to the Mayor and her watchers are fairly classic "lack of strong father figure" behavior; I think that may even be stated by someone in canon.

Here's the thing -- parents have a major effect on how people grow up, and so I think that imagining nonexistent fathers into scenarios is fairly problematic, particularly a character like Faith, who we meet when she's so young, who's practically defined by her reaction to authority.