If pushing through grant money is the volunteer's primary talent, they can just as easily do so without spending all that useful money on plane tickets and training.
The other issue is that money by itself doesn't solve problems. You have to use it to solve real issues. But the Peace Corps doesn't fund research into what the issues are, because that's expensive and unsexy to anyone touting what the volunteers are up to. So you get grants to fund construction of libraries when everyone in the country can already go to an Internet cafe and read Wikipedia.
Peace Corps isn't saving the world, but it does a little in a lot of places and it costs peanuts. If you can do better local work in the same places with the same resources, that's great, do it.
Everyone?
Perhaps you misunderstand what a modern library is - it's a place for accessing information, not limited to books. Most likely it's effectively a free internet cafe or an information centre for a particular school.
Mind you I've seen government funded medical centres without even beds (well mattresses, they had the frames) - so the chances of the information resources turning up and staying put are perhaps slim.