You are 100% correct. All totalitarian societies want to control of their peoples’ children. When the ancient Romans conquered a tribe they forced the leaders and prominent families to send the their children to Rome to be educated on how to be good Romans. After 10 years or more in Rome, they came back as Romans loyal to the Rome Empire.
Muslims did the same. Actually, that was our Indian policy for years. Indoctrinate them young and they’ll be believers forever.