Why drain soaked rice?
Apart from water, rice is mainly made from starch. Starch is initially packed in a crystalline structure that is not soluble. However if you soak it for long enough or expose it to heat, the starch slowly 'unpacks' and binds with water, resulting in a soluble compound. This is called starch gelatinization, and is what you are aiming for when you soak your rice in water (note it gains volume!). But it works in two ways: now soluble starch molecules detach from the rice and go into the water. This is why it gets cloudy. 

The upshot is that this water is full of rice starch, and if you cook it will behave similar to when you add corn starch to water: thicken and form a glue. If you cook your rice in this water you should thus expect a much stickier result, with big lumps of rice 'glued' together. This is not always undesirable! Risotto is an example of cooked rice where we deliberately use this effect (so don't wash or soak your risotto rice).