Why would you start your schools at 6am, I wouldn't take a job that made me start at 6am every day? I would just slowly get tired and less effective.
Now I don't quite understand what you have written here because you just say "we", but assuming you mean work colleagues then I think there is a bit of a difference between someone starting at 8, and making kids catch a bus at 5:45 so that they can start school an hour later at 6:45? That's not waking up at 6, that is out of the house before 6, and while you survived, it really shouldn't be necessary in a 1st world country.
While you did it, there is plenty of evidence that you could have done even better if you weren't subjected to it.
My parents trusted me so they accepted this. I sort of stayed out of trouble, my teachers’ average test scores weren’t impacted negatively and I spent my days coding and hacking (so I got arrested twice .. sue me).
Is private school (in general) worth the cost?
In the Washington, DC, area, there are very good private schools. I doubt that any of them are better than Wootton or Churchill in Montgomery County, Maryland, or such magnet programs as Thomas Jefferson in Fairfax County.