This would make sense if the consequences of sleep loss were more benign. But the penalties for what might be called catastrophic sleep loss are well known. Allan Rechtschaffen has done a famous series of experiments in which rats were wakened to death. Rats deprived of total sleep died in two and a half weeks, after their thermoregulatory systems collapsed. Rats deprived of REM sleep died in five weeks. (No one knows how soon a rat would die if, like the insomniac subgroup Mendelson described, it merely believed it had been deprived of sleep.)
Rats die after two weeks of total sleep loss. They can survive without food for about the same amount of time.