In fact, you can use chlorine bleach to treat a swimming pool or to treat drinking water. Typically a pool is treated at a rate of 3 PPM, and drinking water is treated at anywhere from 0.2 PPM to 3 PPM depending on the level of contamination and the contact time. Chlorine is used in pools and drinking water because it is a great disinfectant. It is able to kill bacteria, algae, etc. Chlorine also makes a great stain remover, but not because of the chlorine itself.
Chromophores can absorb light at specific wavelengths and therefore cause colors.
When chlorine reacts with water it produces hydrochloric acid and atomic oxygen. The oxygen reacts easily with the chromophores to eliminate the portion of its structure that causes the color. There's been a lot of discussion recently about the safety of chlorine in drinking water. It's not clear how safe or unsafe chlorine is, especially in PPM concentrations. Millions of people have died from water-borne diseases, and these diseases are largely eliminated in modern water systems through the use of chlorine.