I could see something like this being very useful for watching out of town sports teams. For the NFL, I might want to tune to the local Fox/CBS station to watch some game that I wouldn't normally get in my market. That is, assuming it's legal...
Fortunately, there are companies offering private mail boxes and forwarding services in most medium-to-large cities, so obtaining a billing address in the market of your choice isn't particularly difficult.
Right, but you'd also need a CC tied to that billing address, one that will presumably be billed monthly, so not a one-time throw-away. So you need a CC and a private mailbox service in every city you want to see TV. But that is really just circumventing the must-live-in-service-area rule, so subject to being found out and cut off.
The limitation on transmitting copyrighted works essentially creates a geographical monopoly with respect to television. Even if you could fly to another city and watch TV for free there, it is a copyright violation for a company to send you the signal from an antenna there. That's also why the Zediva rent-a-DVD-remotely was struck down: even if you own or rent the equipment, it seems illegal for the company to transmit the copyrighted work to you.
The ruling in the Aereo case gets around this because they limit their transmission to people who get the exact same free-to-air signal. There is still a transmission (which is what the dissenting judge based his argument upon), but the practical effect of getting the same content you would get otherwise seems to have prevailed, fortunately.
IANAL so I don't know how accurate that all is, but it's the understanding I've gotten from reading around.