I generally agree with you. I suspect the current weather station hardware is mostly designed to report in to its corporate owners, but that could probably be worked around. Building a decentralized network for collecting weather data should be possible.
The hard part is that turning the raw data into actual forecasts requires a lot of processing power. My first thought was that it could be done by a large distributed network, similar to what was done with the SETI at Home or the protein folding project. My second thought is that there might be enough processing power that way, but it would be too slow to be useful. There's a lot of lag time in that kind of decentralized arrangement. It would likely produce accurate forecast of what happened several hours ago. I'm not sure how to solve that part of the problem.