To be fair, the writing does try to actually show her transformation and does so in a fairly effective way. BioShock Infinite is in some respects a coming of age story for Elizabeth, and shows here turning from a naive girl into a hardened woman. The problem is that time compression (especially in the game's final act) makes this come on really sudden, where she goes from being still mostly the same normal old person, to some sort of fucking psy-ninja in about an hour's time.
I don't think the sexualizing of her was done specifically by Ken Levine, it probably has its roots more in the publisher's influence and/or the artists themselves. The themes and content of the game don't really support making her out as some sort of sex object, and even her cleavage outfit (Lady Comstock's dress) is obviously meant to have far more narrative repercussions than fan service ones. Making Elizabeth Booker's daughter and combining it with subtle romantic undertones may also have been intentional subversion and done to make the audience feel a bit uncomfortable.
In other words, I guess I think Ken Levine is a smart enough guy with enough integrity to not feature a blatant creepy sex doll character just to get his fans hard. I can see why it'd be read that way but I'm not so cynical that that was the intention. You can make similar arguments about any other female character in games, and with those the arguments are more compelling the less complexity and growth those characters have (i.e. the girl rival trainer from the Pokemon games, pretty sure Nintendo wasn't trying to turn her into loli bait, but that doesn't stop the Internet).