Rainwater, with the exception of accumulated dust, is pretty much pure (more or less) water. Irrigation water has passed over hundreds of miles of land containing salt, fertilizers, animal wastes, and insecticides. It evaporates on the land and becomes more concentrated. Lakes with no outlet become very salty, like the Dead Sea and the Great Salt Lake in Utah. The Colorado River is a terrible source of water, by the way.
Some plants, like salt bush and tamarron adsorb salt from the soil. Still, you have got to dispose of the plants, so you are only moving the problem. Also, it takes lots of time.