For over a millenium until 1965 popes wore a papal tiara, the papal crown, at secular ceremonies in the Vatican. There are around 15 surviving tiaras, the oldest dating from the 16th century, the newest from 1963. Paul gave his 1963 tiara to the Catholic Church in the US and it is on display in Washington's RC Cathedral.
Though he never abolished the tiara, he abandoned wearing his own. IN his 1975 apostolic contitution Pope Paul required that his successor be crowned. This rule however was disobeyed by Pope John Paul I, who opted for a rather naff inauguration ceremony which was almost made up as it went along (there had been no rite for the ceremony ready and they had to make one up when he refused to have the traditional coronation).
I am certainly not a conservative Catholic but I regret that the tiaras are not worn any more. Many of them were spectacularly beautiful and very historic. Some of the papal mitres now worn instead of tiaras at the urbi et orbi ceremony are grotesque and embarrassing. If many of the old tiaras had the 'wow' factor, many of the mitres have the 'ugh' factor.
The one above is the oldest surviving tiara, dating from the sixteenth century. It has not been worn for centuries by popes but is used to crown a statue of Peter annually.
The one below is Gregory XVI's tiara from I think 1835.
The tiara below is the Belgian Tiara given by the ladies of the Belgian Royal Court to Pope Pius IX in 1871.
The one below is the Palatine Tiara, given to Pius IX by the Palatine Guard in 1877. It was the coronation tiara of Pius XI, Pius XII and John XXIII. It is the most recognisable of the papal tiaras.
The tiara below was given to Pope Leo XIII by Kaiser Wilhelm I in 1888.
The one below is the Milan Tiara of Pius XI, worn in the picture by John XXIII. (Whereas most popes wore one or two of the collection, Pope John wore most of the main tiaras at one stage, but the Milan Tiara was the one he was most often photographed wearing.)
Below is John wearing his own tiara, presented to him in 1959 and the lightest in the papal collection, weighing just 3 lbs. His election was such a surprise that his native area had not time to get a tiara made for him in time, but presented him with his new, lightweight tiara a year later.
Oops. Wrong tiara. This is him wearing his own tiara. The one above is Pius XI's Milan tiara.
This is the final tiara (to date), given by the people of Milan to Paul VI. As well as a futuristic modern design, it was also one of the heaviest to wear. The picture showed his coronation in 1963.
Or being carried in state.
He stopped wearing it later in 1965, ceremonially placing it on the altar of St Peters. (below)
John Paul II left it up to his successors to decide whether to be crowned or inaugurated. He specified the "inauguration of a pontificate" but a pontificate can be inaugurated (ie ceremonially begun) by means either of an inauguration or of a coronation. He avoided specifying that a "papal inauguration" was the form of ceremony to be used, simply that some ceremony be used to inaugurate a pontficate. Given his love of pre-Vatican II liturgy, there was surprise when Josef Ratzinger as Pope Benedict XVI opted for an inauguration rite rather than a coronation. There was even more surprise when his personal coat of arms controversially broke with tradition by not including a papal tiara, though some versions later started to include the tiara again.
I'm not a conservative (at all) but it but maybe it is time the pope began wearing the tiaras again. They have been sent around the world on a tour and drew massive crowds in Europe and the US, so there is obviously still an interest in them. Some of them are indeed very historic and spectularly beautiful.