I have seen the effects of this first hand, in myself and my co workers.
If you are on irregular work schedules I strongly advise you to do everything you can to get a consistent work schedule. Especially if you are suffering from chronic burn out.
Chronic burn out from work is caused by improper work/home life balance that irregular schedules do not facilitate.
Your employer knows next to nothing about your home life, so why are you letting them dictate your work/home life balance?
Stop letting the computer generated schedules burn you out and go see a doctor to back you up in demanding consistent schedules, or force their hand by getting extra curricular activities such as competitive sleeping.
You are in charge of your own health, and it's up to you to balance work/home life. Without that balance work will always prioritize work.