from a 100% math basis you might be right.. im not aware of studies that show it but there are other things that I think come into effect when you train in the morning.
I learned all of this as an athlete years ago but here are a few things:
when you wake up at 5am to run.. you will not be up until 2am wasting time
you will not be up at midnight snacking away
you will not snack during the day because you are focused on weight loss our your fitness all day
you can not make up a workout that you overslept for
a lot of it MIGHT be mental and thats fine with me... A ton of pro athletes or future pro athletes are up at 5am to get their morning run in or do their roadwork or get their first training session in
if you want to get 3 workouts in a day say cardio, weights, skill training then 6am is the best time for cardio.. noonish is best for weights and night time is the best for skill.. for me and my guys or my type of athletes
I know plenty of athletes doing 4 workouts a day.. basically 1 cardio, 1 weights/strength & conditioning and 2 skill workouts.. if you dont do the cardio in the am it will be hard to do all that..
Now I know this is primarily a bodybuilding board

so some of this seems useless or WRONG but its not.. its just different and hopefully there are some bits and pieces we can all learn from each other.