It's OpenBTS, not Facebook's new project, that developed incredibly cheap 2.5G GSM service on cheap, software defined radio hardware.
Exactly. This idea has been around for yonks. Probably the most visible in international development circles was the Grameen Foundation's Village Phone project. This included small-scale GSM transmitter/receivers along with phones that would be shared on a commercial pay-as-you-go basis.
I met a few people working on a variation of this in Timor Leste, and tried to get some formal backing and traction for this in some Pacific island countries. The bottom line is that it's a no-go scenario, because you have inordinately high regulatory barriers, and the opposition of local telcos, who don't want anyone else hanging off their infrastructure, no matter how good it is for the bottom line.
That made some sense at the time, but today, why wouldn't you build your wireless network on WiFi instead?
Because at the end of the day, you still need to interact with local telcos. You can shim it any way you want, but if a person can't call or text their cousin in the capital, they're not going to pay to use the service.
But that's not reason to give up hope. You should give up hope because the telcos will never let it happen anyway, and even if they do, they'll find some new way to screw you out of accessing an affordable and open internet. :-)