If nothing else they give free exposition. Sometimes the Doctor doesn't even have to be there to have a great episode (Blink), but usually when they try it the results are less than desirable (Love and Monsters). One problem with the new Who is that the Doctor has only one companion generally, Rory notwithstanding. The older series you could have contemporary companions (Barbara/Ian) and an other companion that was out of time (Susan/Jamie). That gave you multiple viewpoints at the expense of sometime a bloated cast. It's become a formula, but it's a formula that works. Would have liked to see the Xmas Special Clara become the companion, but we're getting the modern day Clara so the formula continues.