it's not time that heals all wounds - it's REM sleep

Not all sleep is REM sleep.  It is the dreaming phase of sleep which you go in and out of depending on other physiologic variable.  


The other consequences of too little sleep (from WebMD):

• Impaired memory and thought processes.
• Depression.
• Decreased immune response.

Sleep deprivation also magnifies alcohols effects on the body, so a fatigued person who drinks will become much more impaired than someone who is well-rested. Sleep deprivation also increases pain perception on pain simulation testing. Caffeine and other stimulants can temporarily overcome the effects of severe sleep deprivation, but cannot do so for extended periods of time.