DA2 was set within the confines of a single city. If that is the case in any future games, then no, I would not be opposed to a prostitute character continuing to work in that fashion.
But I wouldn't call it a career. As I said, most people that enter the sex industry don't wish to stay there for their entire working life.
Quite right. Like I said, the story dictates.
I agree making a living as a sex-worker isn't usually a long term career, even for the willing. Courtesans in Renaissance Venice, say, looked at it as a way to make their fortune, and having made it, invested it and lived very well off it after they retired, or went on to other things (often prestigious marriages, sometimes even to ex-clients). I know being a Courtesan is not quite the sort of sex-work we are talking about, but if BW wanted realistic portrayals of sex workers with a basis in history, they could do worse. For some women, it was the family business, for some, the best of a bad lot of choices, for some, their making and for others their undoing.
As I say; the problem is integrating it into the game. For better or worse, it's not the sort of thing that comes up in casual conversation. Even if you're sitting around a campfire swapping stories.