If the state is determined to track or identify the user, I agree this doesn't help. It might delay them a little. But I don't mind the state investigating people for legitimate reasons (e.g., under a warrant); I'm not trying to protect criminals. Also this won't protect people persecuted by repressive states - that's a very valuable goal, but outside the scope of this idea.
For dragnet surveillance I suspect this would work, simply by adding enough complexity to the task that it's not worth it for one more data point among billions.
Of course anyone could make a social graph based on my phone calls and learn a lot that way, but I don't think anonymous phone calls are possible. If I want to receive incoming calls then I have to give out my phone number; my name and number inevitably become associated. (I can think of a few weak solutions, such as having many phone numbers, but that's imperfect and impractical.)
