Actually, my claim is not that the cost would be more than a dollar, but that private carriers would flat-out refuse to deliver to many locations in the US (and with good reason; it wouldn't be profitable). We already see this problem with the lack of internet connectivity in many rural areas.

So if you believe that this sort of communication is a fundamental right for all citizens, than the service needs to be provided by the public sector. It's impossible to build a profitable business in the private sector out of it.