This is gonna be the thread where we talk about stuff

SeaWyrm you are talking about an internet game that, on last page, you said you haven't yet taken part in. Have you at least read a game that's had roleplaying in it? That'd probably be something you'd do before becoming 100% certified-convinced.

You guys know you could roleplay based on the flavor of a character's description, not based on the role. Like "you are Mildred Robocks, a wealthy trophy wife who drinks plenty of wine and gets drunk all the time, leading to wild outbursts of rubbing up on people." This flavor is assigned independent of the role. Maybe she's a town doctor, who performs sexual healing; maybe a cop who coaxes information out in moments of passion; maybe she's a mafia roleblocker for hookery reasons; maybe she's a mafia janitor who has connections to a wine manufacturer and will once a game turn someone into a bottle of Château Soylent.

To be a roleplaying game, the mechanics need to interact with the story AND the story needs to interact with the mechanics. Mafia mechanics only interact with the story by providing a vague setting/situation (which doesn't really count) and by removing characters from it periodically for reasons that don't really have anything to do with what's happening in it. The story doesn't interact with the mechanics at all, except if you decide to make your game mechanics decisions based on the story rather than based on, say, strategy. Which you can do, but you could also do that with any game.
Chess, for example. You can move the pieces around based on a fiction, sure, in which the knights are actual knights and so-forth, but if you're playing against an opponent who's not in on it, they'll beat you solidly and laugh because they're using actual strategy. Their move decisions won't likely do wonders for your story, either. And if they ARE in on it, you guys aren't really playing chess anymore, you're just telling a story and moving bits of wood about.

Or, to throw your example back at you, you could roleplay while playing, say, softball. You could make up descriptions based on the field positions. Like "you are Anthony Pieterson, a wealthy corporate man who built his own fortune and has no patience for others who don't share his luck and business acumen." Maybe he's a left-fielder who catches the ball with diving leaps of daring-do; maybe a pitcher who pitches fastballs as smoothly as he pitches tricky business propositions.

Can you have FUN playing Mafia and roleplaying alongside? Heck yes! And I'm not saying you shouldn't roleplay with Mafia, either. Roleplaying probably brings a lot of enjoyment to Mafia. But Mafia doesn't really bring anything to the roleplaying. Because it's not a roleplaying game. (Which is different from saying it's "utter rubbish" as a roleplaying game, yeah. But this is what I really meant. I think the "utter rubbish" bit comes from the fact that it looks, superficially, like a roleplaying game, so it's utter rubbish as a roleplaying game in the same way that a toothpick is utter rubbish as a match.)

And for what it's worth, no, I've never played it on the internet, but when I first played it with people, it was under the (extremely naive) impression that it was meant to be a roleplaying game. This quickly proved to be an exercise in frustration, on multiple occasions, with multiple groups of people. So I am talking from personal experience here. But even if I wasn't, well, I've never played Stratego before, or Baccarat, or ice hockey, and I can still tell you that they're not roleplaying games, either.

Having said all that, I do want to clarify that I'm not saying that Mafia not being a roleplaying game makes Mafia+roleplaying bad or wrong or something. I'm sure all kinds of awesome stuff has happened from that combo! It's probably a lot of fun.
Whenever I play Diplomacy I like to adopt a persona and write all my in-game notes to the other players with an in-character voice. I do this myself and am disappointed when they don't return in kind. This is a perfectly legitimate thing to do and it makes the game more fun. It also doesn't impact my strategy one whit - I still make the alliances I'd make anyway, backstab the people I'd backstab anyway, and play just as strategically as if the added flavor were missing. Diplomacy is not a roleplaying game. But that doesn't mean you can't have fun by roleplaying alongside it. I don't mean to imply that the same isn't true of Mafia.

tl;dr:
I DO mean to imply that it's foolish to try to play it as though the story you tell is important and consequential. It isn't, it's just flavor.
That's all I'm really trying to say, here.