Remember we never see (except possibly during the closing scenes of RotJ) C-3PO in a setting where his function as a protocol droid would be beneficial.
His job is as a court functionary, not a fugitive smuggler or warrior in a rebel band.
As to everyone speaking common, Jabba the Hutt didn't. Nor did several of the people in Mos Eisley so not everyone in the Star Wars universe speaks the same language.
The fact that everyone (or almost) the main characters come into contact with does may be either a fluke or designed that way to make the movies easier on the audience. A conversation that takes over twice as long as it should because every sentence has to go through a translator doesn't make for very good cinema after all, so I call artistic license here.
The fact that Leia had a protocol/translator droid with her on her diplomatic mission indicates to me that she did expect to need those services in some capacity. It just never made the cut.