Most people have highly adaptable bodies and can train themselves to be a "morning person." If a person were to stay up until 2AM, there's no way they'd want to wake up at 4AM. They would therefore see themselves as a productive night owl.
I disagree. If it were that simple (with some work, obviously), more would easily be able to train themselves to be "night people" to work overnight shifts. And my experience working nights disagreed. Some folks just cannot handle the sleep and waking times of the shift, others get to a point that they have trouble being productive. A few find it unsafe to drive home afterwards.
I think we are flexible and adaptable to a point, but there is a limit before you find health and sleep suffers a bit too much. For most, nights would push the envelope, but the early mornings do it for a few of us.
If it were possible to train yourself to be a morning person, then I would have done it by now after several years working 1st shift (8 AM start). Previously I was working 2nd shift (2 PM start). I never really have gotten used to getting up to be at work by 8 AM. I do it, but I always feel sleepy until about noon. Last week, I had to cover for an absent coworker and worked 2nd shift for the first time in years. All last week, I felt more alert, I was more productive, and I slept better.