Prefacing my comments with the fact that I haven't flown in 3 mos, here's my thoughts.
I saw a piece on NBC where the one and only controller in the tower stepped out, and got locked out. he (presumably) was locked out for XX minutes, until security came and let him back in.
So, you are a pilot, and approach at another airport clears you in, maintain until established, contact the tower, and there's no one there to contact

Do you, A, call approach back and tell them no one in the tower, or B, keep on going, and hope the controller gets back from break? B. which means that most of the time the missing controller will never be reported.
Also, there was the instance in Australia, privatized, where the controllers shift ended and he went home. Unfortunately, there was no replacement, for a couple of hours.
If you have a flight plan filed, IFR, and there is no one in the tower, do you proceed, or sit there until someone answers? Keep going, call FSS when you get in the air??
If it saves money, who's money does it save? The FAA's? Who pays for the contract controllers? The local airport authority? Who pays them?
Lots of questions, no answers from me. It seems, fundamentally, that the governance of air traffic is a federal responsibility, and should never be contracted to a private company. Kind of like the police department, the FBI, the Army.