Give it a few more decades and they'll be wired just like everyone else.
And data rates of > 1 Gigabit for wireless connections are readily achievable these days. [1]
People say infrastructure is too expensive to build, it's not. When you have a discerning customer base with the purchasing power to demand it, infrastructure is the only way to serve it. Wireless cannot support that. As soon as the developing world stops being developing, in will come the telcos to build real kit.
#1 - The United States is wired for legacy reasons, our infrastructure was built 50+ years ago when wireless voice and data for the most part did not exist.
#2 - When I say "sparse" I'm referring to density of the target population, as in, the number of households per square mile.
It does make sense to run wired connections to dense urban populations, the cost-per-connection, particularly measured on a bandwidth-per-drop-per-dollar basis is great. Also, if you already have cable (either pairs of copper, or coax-for-TV) running to those people's homes, you've got a foundation for delivering data.
For most of the developing world in the next century (excluding the cities), communications, data, and entertainment will be in the form of wireless (Satellite, 3G, or directional 50 GHz+ data drops for backbones).
We won't be running cables to supply communities in the African countryside with high speed Internet. (We also won't be running it over 3G/LTE - which wouldn't be most people's choice for a wireless data backbone these days)
Wired connection is extremely expensive to deploy and very time consuming too, wireless, not so much. As a matter of fact there is no "nation-wide" wired internet service here, only local providers. New wireless providers are popping up almost every year...
It's been years since I've had a landline phone. I'm sure I'll eventually drop my landline high speed internet connection too.
In the developing world, cell towers connect to other cell towers wirelessly. That's a hack. It's the reason why hotel Internet blows. Not its proper use case, engineering-wise. Service sucks but the customer base isn't discerning enough to notice and wouldn't be able to afford better.
We have Clear Internet service in Atlanta. We had it for awhile, but crappy reception due to trees even though we were well covered by three towers made us go back to cable. Dialup would have been better. I had another friend within eyesight of a tower, he dropped it too because service got so crowded and bad that he couldn't stand it.
Current wireless technology could never replace wired and deliver the same quality of service that wires do. For proof, head down to your local Starbucks and try to get work done. I've not seen one yet where the connection didn't cut out at least once an hour. Radios degrade over time, copper doesn't.
I'm not sure it will be ever be profitable to run landlines. The big issue being that there wont never be public and private monopolies again and that you dont run a line to a single costumer.