After the death of Pope Francis, upcoming canonizations and beatifications were suspended, with the note that these events would be rescheduled when a new pope is elected.
Why is that?
Currently only canonizations need the presence of the pope, while beatifications are often celebrated locally without the pope's physical presence.
Canonizations and the Universal Church
One of the primary reasons why the pope presides at a canonization is because of its universal nature. When a man or woman is declared a "saint," the pope does this for the "whole Church."
Only the pope can make such a wide-reaching proclamation.
In a certain sense it binds all Catholics to the belief that this person is a saint.
The Catholic Encyclopedia explains that "Canonization, generally speaking, is a decree regarding the public ecclesiastical veneration of an individual. Such veneration ... is universal in the sense that it binds the whole Church."
Many theologians also argue that canonizations are an act of papal infallibility. This means that the Holy Spirit protects the pope from error when he proclaims an individual a saint.
Beatifications and the local Church
On the other hand, beatifications do not hold the same authority, but they still require the permission of the pope.
The Catholic Encyclopedia notes that "beatification is a permission to venerate, granted by the Roman Pontiffs with restriction to certain places and to certain liturgical exercises. Thus it is unlawful to pay to the person known as Blessed (i.e. the Beatus, Beatified), public reverence outside of the place for which the permission is granted, or to recite an office in his honor, or to celebrate Mass with prayers referring to him, unless special indult be had."
This refers to public, official veneration; the faithful may individually have devotion to a certain Blessed, even beyond their place of birth.
One example of this is how St. John Paul II was initially only venerated in Poland and Italy at the moment of his beatification, but shortly afterwards the bishops of the United States were granted permission to allow Mass to be celebrated on his feast day.
This is also why beatifications are typically celebrated locally and do not require the pope's presence. It is not a "universal" decree and only reserved to local piety.
Beatifications are not infallible, and there have been certain individuals who were never canonized, due to new information being learned that disqualified them.
Benedict XVI made changes to the processes of beatification, particularly emphasizing their local nature.
Wherever Beatifications take place, in Rome or elsewhere, it is necessary to show clearly that every Beatification is an act of the Roman Pontiff, who thus permits ("facultatem facimus" in the current beatification formula) the local cult of a Servant of God, making his decision public in an Apostolic Letter.
Read Benedict XVI's changes here.