Why are fish constantly in motion?
A research, detailed in a 2012 issue of the journal PLoS Biology, suggests the fish do indeed take naps and can experience sleepless nights.

Another research with Pacific sand lance species, found them utilize a one of a kind methodology of tunneling into sand to rest and moderate vitality, and to maintain a strategic distance from predation.

Therefore, we can assume that fish sleep cannot be related to a terrestrial. As @Zxyrra has mentioned, with the currents being random in their direction, we can connect the reasoning of the continuous movement of the fishes as an effort to stabilize themselves. 

On the aspect of any evolution or biological reasoning, fish sleep is still an ongoing research in marine biology. An interesting research have opened up a case in which through evolution, cavefishes have lost sleep. Information from this research could help you understand the evolutionary relationship of fish and sleep, in atleast, a broad scale.

UPDATE: Unique method of sleep in dolphins.

At the point when it's an ideal opportunity to rest, a dolphin will close down just a single side of the equator of its mind, and close the inverse eye (the left eye will be shut when the correct portion of the cerebrum dozes, and the other way around). Amid this time, the other portion of the cerebrum screens what's going in nature and controls breathing capacities. This process is termed as unihemispheric slow-wave sleep.