https://phys.org/news/2018-06-fur-insight-function-rem.html

This 'behavior' has been found to occur in many different animals. Sleep states are defined by changes in occurring in the cortical/thalamic complex. With 2 hemispheres we have 2 cortex's, and there may be nothing in the physiology, outside of the connectivity between the 2, that says that both have to sleep at the same time. I suspect that it is highly likely humans already can sleep this way also but we are unaware what it is when it happens. Otters can wake up very grumpy and disorientated and that is why you should never poke a sleeping one. Who hasn't experienced waking up feeling very out of sorts?

Water is a much more efficient medium at drawing heat from a body than air so maybe this type of 'potential' sleep state may become more well defined and the norm in dolphins and other mammals that sleep in water as a mechanism for keeping the brain warm.