Why do you think Hamid arranged the narrative as Changez’s conversation with the reader? What does this allow the narrator to do that might be otherwise impossible in alternate, more traditional narrative forms?

I don't think Hamid arranges the narrative as a conversation between Changez and the reader but, rather, as Changez's conversation with an American who may have been hired to intimidate or even kill him. Changez refers to his conversation partner as "sir" and alludes to the specific time and place in which they eat, and so we can see that he is not speaking directly to us. This conversation partner is also somewhat paranoid, thinking that the "misfiring exhaust of a passing rickshaw" is a gunshot and worrying about the "few figures [...] in the gloom" walking behind them on a public street. In fact, Changez tells this American

[...] I was warned by my comrades that America might react to my admittedly intemperate remarks by sending an emissary to intimidate me or worse.

It seems possible that the American with whom he's been speaking this whole time is such a person, as, in the end, that American reaches into his jacket and Changez "detect[s] a glint of metal."
Changez is, obviously, critical of America, but when Hamid presents those criticisms within the framework of a friendly—at least on the surface—conversation, they seem much more palatable to the average American reader. Were these criticisms directed directly to, or even AT, us, we'd likely be much less receptive of Changez's ideas. We might get more defensive. However, we get to be a fly on the wall of someone else's conversation, watching them squirm, perhaps, but it's better than squirming under Changez's words ourselves. It also gives us a chance to recognize the American listener's defensive and somewhat paranoid behavior: he is wary of the waiter, the food, other people, everything. We might even recognize the fact that we, ourselves, could feel similarly in his situation and because we see how paranoid he is given Changez's tranquil and reassuring demeanor and history of nonviolence, we realize that this feeling is somehow both self-centered and ridiculous, helping to prove Changez's points.