So, if one decides to "self position" ie. at your own convenience rather than the convenience of the employer - is this time now not contributing to any personal fatigue?
Many many things contribute to personal fatigue. It's called having a life. You may choose to drive around the M25 every working day, I may choose to commute to base at my leisure and live in a hotel 5 minutes from the crew room. You may choose to raise pigs and may be found shoveling pig manure whilst I leisurely board one of my commuting flights listening to Bach on my noise cancelling headphones. You may choose to make a baby with your wife which will guarantee that you will not sleep properly for the coming years, whilst I may choose to leave all the family hassle at home for my five day stint at base.
As long as our performance in the flight deck does not suffer, who are we then to mind each others private lives?