I think it is because even an English speaking audience can figure out what is being said... and remember, Michael breaks into English pretty quickly once he sees McCluskey is more interested in the best veal in the city than he is in the conversation.

The first piece of Italian dialogue is when McCluskey orders the veal and Sollozzo says "Capice?" to the wwaiter who says, "si."
Then he turns to Michael and points to his face (which McCluskey had bashed) and says, "Mi dispiace (I'm sorry)" which Michael waives off.

Then he says "Io, Io voglio pace" (I want peace)
and .."ma tu padre pensa d'antica" (your father thinks the old way," the emphasis is onthe words "dispiace," "pace" and "padre pensa antica"
those phrases are pretty easy to figure out, and of course then the conversation turns to English.

In sicily the conversations are more complicated, and the sicilians are speaking rapidly to one another, because they speak the language. When Sollozo speaks to Mike in the dialect he speaks slowly because he knows Mike struggles with it.