Reason for aquatic plant roots
Among terrestrial plants, roots have two major functions - obtaining water (as well as nutrients) and anchoring plants in place. (However, roots may have other important functions as well.) Aquatic plants obviously don't have a problem obtaining water. So roots presumably function primarily as anchors.

There are rootless planktonic plants that float on the surface of water bodies. However, aquatic plants like cattails and water lilies are probably a little more discriminating in their habitat preferences. Imagine a rootless water lily being blown by a hard wind into a patch of water lilies, which block out the sun.