A strong argument for getting the third world online is to help create more jobs. This sounds like a corporate sound bite, but it's a complex issue where job opportunities are a few degrees removed from providing broad access to the internet in and of itself.
In a lot of developing countries the only jobs that are available are supporting existing industries that are heavily dominated by mega-corporations that are much more focused on resource extraction/profits than they are on developing human capital: Clothing industry in India, Tourism in Mexico/Caribbean, Mining Natural Resources everywhere.
While much of the initial profits and use cases for bring a country online are frivolous and tend to mirror 1st world consumption patterns, the internet access is critical infrastructure for supporting a more decentralized economy.
As adoption of the internet, and telecommunications infrastructure more generally take hold, economic opportunities that didn't exist before will start to emerge: Mobile payments in Kenya, Bitcoin merchants in Chile, or even the selling US produced content in Cuba (the "paquete").
Access to decentralized communication networks enables people in developing countries to participate in the economy on more favorable terms and enables people to work and start businesses without having to work through existing gatekeepers (I think this is why people have responded so negatively to the internet.org model).
I would love to see some studies on internet or network driven economic development, maybe as an alternative to Import Substitution.
Second, in many ways the developing world is better leveraging the internet than the developed world. Travel is a huge issue in the developing world so being able to do remote transactions becomes far more valuable. Access to education and professionals is more limited so information becomes more valuable not less.
Or why doesn't BT in the UK just build its own mobile network instead of buying EE
Because for profit companies want to make as much money as possible and spectrum is limited. Which is more or less why buying an empty field in the Brazil is ridiculously cheaper than the same sized empty field in downtown London.
You don't need to start by building a nationwide network when you start out. 1 Cell tower can handle a little over 1200 calls at the same time and cover up to 1,500 square miles using 2002 teck. So start with one tower in the major city(s) for a few million and add towers as needed after that with the revenue from customers.
Which is why there is a cell network in every country. The problem is a few towers is not going to cut it once someone is covering the country.
PS: Building a modern tower in the US costs ~300k USD as a baseline including equipment and construction costs (though you can have more than one network per tower). Covering the UK wold cost at a minimum ~30million USD for the towers assuming ~1k square miles per tower. Less if you include significant gaps, laying the ground network is adds costs. But you would probably pay 10x just for the spectrum and you would want a much higher density in city's, and land is not free etc.
Heck, having better communications directly helps with food and jobs; you have a much easier time finding the guy who needs a worker or has a spare bag of rice if you're both online. Might even help with "clean water"; you can find information on how to make water potable and sanitation in general.
I couldn't tell you for sure whether getting smartphones to a village is a higher priority than installing a good well, but the smartphones are worth enough that I don't think that either choice is obviously superior.
Then they would travel from village to village to help locals with various issues (saving crops from pests, figuring out minor illnesses etc).
Basically they were carrying around the equivalent of a library in a shoulder bag.
More recently an article mentioned a farmer somewhere in Africa that had gone to a netcafe to look up solutions to his failing crops.
All these efforts to put smartphones in the hands of starving people seems motivated by mega-corporations eager to "open up new markets", exploit vulnerable people, and increase their tracking datasets using people too naive to know any better. Most Americans resist privacy invasions because they've been a bit educated on the topic, so let's move on to people who don't know better?