If I am honest, I have only heard about Frederik and Ingrid's condition that they wait until Anne-Marie is 18 to get married.
However, I would assume that it was due to the political tensions at the time. The whole decade of the 60s was a tumultuous period for Greece's political scene because of the rise of Papandreou who at the time was considered too progressive and the tensions with the right-wing conservatives. The military coup of 1967 was brewing for some time, so perhaps Constantine getting married and having children as soon as possible would send a message that the monarchy was strong.
I think there is a missunderstanding here, Andreas Papandreou (the one who took away the royal family's nationality from their passports) was outside the country back then and his father, George Papandreou, was last seen in the political scene of the country in 1962. I'm not sure about his role on this, I don't exclude it but I'm not sure.
But I understand what emtishell said about Konstantinos and Anne-Marie
He certainly could have been, I donít think there is any law (written or unwritten), maybe he just felt he didnít want to do it without the woman he loved by his side? Certainly in some ways it would have been easier for them to start out together, and build their partnership along with their reign.