Timothy served in Corinth so that Paul was free to preach. Timothy served Paul, yes. But the 2 letters left to us are Paul's tender solicitation by careful thought and prayer, of his son's life in God and its responsibilities. Timothy stayed in Ephesus to keep that Church in the order of Paul's apostleship. To that hub they were utterly flexible and completely linked to each other.
Discipleship is the way of authority, but it is a gift of loving liberty, of sanctified safety.
It is not a spiritual excuse for tyranny.