The British monarchy only survived into the 20th century as the embodiment of British public school values.
It seems to me that the British system was based on a romanticization of the kind of collective child-rearing the Spartans practiced, where boys were taken from their families and raised in barracks to turn them into hardened warriors... and emotional cripples. The upside of all that emotional deprivation and steely emotional control is to convince you that you are a stronger, superior being to the soft people around you who have feelings. The downside is it makes you insufferably arrogant.
And what if you really aren't superior ? When the Spartans were smashed by the Thebans at Leuctra, when they saw that their system really didn't make them stronger, when they learned that free men can outfight militarists didn't they question the price in human suffering their system asked of them ? What is all that stiff upper lip emotional deprivation worth to be king of a minor power ? What was all that sacrifice and loneliness for since you're not really superior ?
Charles strikes me as a man who feels cheated out of a childhood, out of a normal life, out of the simple freedom to marry the woman he loves, and for what ?
Not just the boys. I have a female British cousin who was sent away to school at the age of seven. As you point out, I think this is the same age at which the Spartans sent their boys to the army.