The thing with Dani Alves is that he's always been a maverick kind of player, it's difficult to imagine how much you could coach into him at this point.
Evra always said about how much he learned with Juve in his short spell, but with Dani Alves he still imagines himself as this marauding wide player who will join every attack. I'm not sure it's in his DNA to be an authentic right back or wing back, and I'm also not certain whether Allegri is even trying to reign him in much. In games where the opposition is pinned back he seems to be allowed to do whatever he wants, which is fair enough.
I think once he gets used to the movements of the team he'll be more useful, but you have to make smarter passes in Serie A than you do in Spain.