Throwing a bit of anecdotal evidence out: throughout high school I had to get up at 6:45 every weekday for four years, and constantly felt tired throughout the day, but it cleared up at night and I'd be energized at 1am. I had to take naps after school, but even if I didn't I'd still be unable to sleep at 11pm. Something about everyone else around me being asleep and not distracting me allowed me to focus on things better.

Now I have a job with very flexible hours so I go to sleep at 2am and wake up at 10am like clockwork. I feel and perform much better all around. I'm convinced that if I had had a sleep schedule that worked for me in my teens I'd have been able to achieve much more than I did.