The Eastern Bishops wear mitres which look a great deal like crowns, but it is understood that this is a symbol of their ministry, not their worldliness. The first western bishops wore mitres resembling crowns as well, but they abandoned them due to the cold northern climates. It may stand for worldliness to you, but this is *a posteriori *symbolism and NOT what the triple teared tiara represented when it was placed on the Pius XII or Paul VI head, and certainly not what it stands for when the statue of St. Peter in the Vatican is crowned every year. Is the Vatican celebrating St. Peter’s worldliness when he is crowned, or are they celebrating his ministry? Is “Prince of the Apostles” a reference to his worldly power or his role in founding the Church. We’re talking apples and oranges here and I think you’re aware of that. I think we know full well what the world today would see a papal coronation as being and representing: it’s impossible to keep a note of triumphalism out of coronation and while we do hold the fullness of Truth, we receive it by Grace, which should be grasped with accompanying humility.
The requirements which Paul VI set down were meant to be a guidline for future elections. If he thought he had no control over how a pope was elected and initiated he would never have written them. his own election and coronation was over with. This may well be so, in terms of his hopes and his prudential judgement, but I think HH Pope Paul VI also understood that this would NOT be binding on the prudential judgement of his successors. HH Pope John Paul II also made changes in how his successor would be elected. For all intents and purposes, HH Pope Benedict XVI may do the same for HIS successor (God forbid that should be occasioned any time soon). As for the coronation, Popes can freely modify, alter, or entirely dispense with parts or all of it. It isn’t a part of the deposit of faith and it isn’t even a sacrament (if he isn’t a bishop already when elected, the man elected pope is immediately ordained by either the Camerlengo or the Dean of the College of Cardinals, I forget which).
I’m also not saying that these things are necessary, but symbols like this are important. The Church has always understood that, hence the beauty of it’s Church buildings, altars, vestments and music. We like to think people understand the extent of the Petrine ministry enough that these symbols are superfluous, but then people often say the same about the liturgy and transubstantiation, and getting rid of Eucharistic Adoration hasn’t done much for people’s belief in transubstantiation, has it? I don’t think that an Eastern Orthodox Patriarch is leaning on his jeweled mitre as a “prop” anymore than the Church uses polyphony and gregorian chants as props in the liturgy. They are aids, and important and useful ones at that. They do matter.