I'm sure there are also situations you could find yourself in where it's useful to know how to acheive maximum endurance. All I can think of at the moment are stuck above solid IMC (without IR/instruments) which is expected to clear, and lost at night - neither particularly likely, or situations I intend to put myself in, but that doesn't mean I don't want to know the figures just in case.
Hollo
I dont disagree with why you may want max endurance so am not trying to discredit it. Normally pilots will need to stay up because they have had stronger headwinds than planned to get to their destination. Maximum endurance will not help you there.
Someone stuck above cloud in a pure VFR aircraft would be ill advised to sit there waiting for the clouds to hopefully disappear.
If my flying involved going nowhere and staying up for as long as possible for as little money as possible I would probably buy a motorglider and only use the engine when I needed to.
Practically saving fuel and thus increasing range has more to do with trip management than engine fuel burn management that was all I was trying to say and that involves so many other vital factors other than how you lean the engine.
Pace