I actually enjoy playing as a freelancer, rather than as someone who is affiliated with a certain criminal organization. Because I believe, in that way, we're offered a much more wider point of view on the atmosphere surronding our protagonist. For the best example, I really enjoyed Niko as a protagonist, and for storywise, stepping in the shoes of Niko doesn't bore you as you get to work with a lot of different people, respectively witnessing a lot of three-bit scums trying to survive in the harsh world of Liberty City. Basically, Niko worked with Russian Mafia, Jamaican Posse, a fierce Bohan female drug dealer, Irish Mob, Pegorino Family, Jon Gravelli and much more I can't tell. Likewise, I enjoyed the stories of other freelancer hired guns like Claude, Vic Vance (to a certain extent, he was working freelance).
Back to the topic, nonetheless, I feel like justice should be done with a GTA game solely focusing on the Italian Mafia. Sure, we have seen this concept a lot, some of them were really accurate, and stone-figured (for example IV did a really good job on the Nosa Costra with The Commission, they played a major background role in the story as well), but I mean something should majorly concern on the Mafia, and would do the justice. I believe, Liberty City Stories was supposed to carry out this concept, but the game was weak on doing it, and didn't shed much light on the topic by including a sold, figurative mafia model (after a certain point in the story, it focused on Toni saving and kissing his precious Sal's ass :W).
In short, I am not the biggest fan of mafia-centric stories, but I wouldn't say "no" to a GTA game focusing on the mafia like Mafia series (I'm a huge admirer of both games) did.