My question is about why aquatic plants have roots. At first they seem a bit superfluous to me because leaves of the plants could just absorb nutrients directly from the water thereby skipping a need for root function that land plants have to pull nutrients from the soil. I then wonder if nutrient trafficking is the reason for the root system as diffusion may not occur efficiently through thick leaves.
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.