"Early in the morning" ...
Young people do not get enough sleep. At Stanford several years ago they did a study and required the men's basketball team to sleep 10 hours a night. All their statistical metrics improve.
It's even worse to get kids up in high school for 6 a.m. practices or, even worse, 7 a.m. Saturday morning runs. Kids need sleep, and they're not going to bed earlier -- or not by enough -- to do something at 6 a.m.
At best, a player would wake up at 5 a.m. for a 6 a.m. workout. To get the 10 hours of sleep they need, they would have to go to bed at 7 p.m.
I have always tried to let my players sleep. My preferred Saturday practice time is 11 a.m., and if the gym is occupied on a weekday, we would not practice rather than try to go before school. (It also disrupts the entire family in a high school setting.)
The point of getting up early to run escapes me completely. OK, maybe shared sacrifice bonds a team, but what you're really after is maximum performance, and that comes from well-rested athletes. If you really feel the need to pound your players into the ground, have them run or practice at 9 p.m. They're not going to sleep until midnight anyway.