As someone who notoriously stays up late, I can finally say it is a bad tradeoff. For 8+ years, I have gone to bed after midnight. For a good portion of this time, I was going to bed around 2am. Only in the last year have I started going to bed reliably before midnight. Now I realize that staying up late (at least for me) is trading your fresh, creative hours in the morning for sluggish robotic hours in the evening. I was wasting my Most productive time of the day.
My ability to think creatively is significantly diminished in the evening, and staying up late to get a few more of those hours at the expense of a productive morning the next morning is just a bad deal.
Staying up late does not produce additional “work” hours, they are traded against the energy level of the next morning (perhaps the next few mornings, depending on how sleep affects you).