* About the horizon problem: You need a tower which is 90 meters (270 feet) high to reach a 40 km receiver. It exists but it is pretty costly ... and hugly.
* About the power problem, this is regulated. For Wi-Fi I think it is around 80mW. It is not much.
* About glossing on math. You are right about it, but after all this is well known: The idea is used heavily in astronomy exactly for this purpose since 10 years. No need to reinvent what more gifted people have already invented.
* About the horizon problem: You need a tower which is 90 meters (270 feet) high to reach a 40 km receiver. It exists but it is pretty costly ... and hugly.
* About the power problem, this is regulated. For Wi-Fi I think it is around 80mW. It is not much.
* About glossing on math. You are right about it, but after all this is well known: The idea is used heavily in astronomy exactly for this purpose since 10 years. No need to reinvent what more gifted people have already invented.