Flew ACMI as a Maintenance Rep for 4 years, chased aircraft around the clock for years prior. I had many 40 hr duty days as a young man and caught my sleep when I could. When doing the flight mech thing, would purposefully stay up to sleep during an 8 -10 hour leg (freighters) so I was on my game when it was time to step up to plate. I would see 3 crews quite often sometimes 3-5 legs before I saw a real bed. Having said that, ACMI being even less reliable than sched long haul and I did the best I could do to have a rested mind and body when my duties were expected of me.
As for the family statement, well I put my wife over my job and quit. Took less pay and concentrated on a different path (still an AMT). I am back making 40% more pay than I earned as a MX rep and see the wife every night. There is no reason not to make every reasonable effort to show up to work for a safety sensitive position well rested!