The problem with wireless is mainly physics: at the higher frequencies that could be used for high-throughput links, you have problems with water. Basically, the signal attenuates very quickly in water (by heating it, which is how a microwave oven works), and so things like plants, fog, rain, etc. all cause problems. Trying to deliver wireless service to homes is going to be expensive -- you're going to be setting up a lot of APs in strategic locations that have line-of-sight to your nearest base station.

It's not impossible, just hard. You also have to deal with airspace e.g. if someone decides to put up a new building right through one of your beams, you need to somehow get around that building, which could be hard. The only people I know of who are doing wireless broadband are doing it in very rural areas, where they can follow the electrical lines, which have nice, clear paths through the forests. Their biggest problem is regulations -- they cannot put up towers because of rules about visual appearance.