Response to Thrasymachus and Axiomatic Assumptons: I think that Socrates did not go straight to the "distasteful core o f Thrasymachus'" argument because he is trying to make it relatable to the rest of the group, who have not spent as much time thinking about these things as he has. I think this is one of the most impressive things about Socrates as portrayed by Plato because it shows that he is a multi dimensional and not just an abstract thinker. 

Response to Beginning the Republic: I think that the structure of the dialogue may have something to do with character development in the sense that it is showing how "long" it can take to change peoples opinions on an issue. I as of yet have no proof for this, but I'll do my best to find it and if not, oh well.