If reducing delta wave sleep by 10% significantly decreases performance on memory and reasoning tests, why should reducing delta sleep by 90% fail to decrease performance?
Lots of studies are done on sleep, but they are never as extreme as polyphasic because it would be considered unethical to perform those studies. Those few insane people like me who actually did go polyphasic don't get scientifically tested.
It did work for me but I recognized that my performance had decreased because at the time I was in memorization-oriented schooling and using Anki to manage my memorization tasks. With the help of Anki, I could see quite clearly that my memorization abilities had decreased.
It was also never a natural state. It was a constant state of heightened autonomic response - fight or flight. Especially at nighttime, my body was surging with corticosteroids. This stress response is what provides the capability to stay awake so long, but it comes at the price of high-level thinking and memorization.
Typically in nature, humans will adopt polyphasic sleep in times of war and other extremely stressful situations. This is adaptive because their life is threatened. This is not the case for the modern knowledge worker.
There is tons of science on sleep. The polyphasic people base their theory on the outdated and discredited idea that we only need REM sleep. This has been categorically disproven by modern sleep researchers. Slow wave sleep provides many benefits, the most clear being improved memory but also better performance on other cognitive tasks.