There's one thing that is obvious - getting marred in the Catholic Church is not like getting married outiside the Church. Why? If two Catholics should marry each other then to get divoced they need an annulment. Whereas if a Catholic and non-Catholic should marry (or two non-Catholics) then no annulment is needed - what does the Church have to do in their relationship?
To myself, this is obviously a hold-over from when the Church was a government and, in some cases, was the government. And still, before 1500, most countries were willing to recognized the supremacy of the Catholic Church. So they did not do marriages, except where one or both of the parties were non-Catholic. Because that was the right and privedledge of the Church - to whom all countries held (questionable) allegiace.
In Immortale Dei Leo-13 said that all people have two government - civil and ecclesiastical. And some / many of what he said were throw-backs to Pius-9 or earlier. Hence, part of what he said was how the Church would deal with non-religous states - obviously, in Leo's mind, the Church would rule in religious matters while the State would rule in Civil matters.
But there has been many changes since the nineteenth century. In 1910 the House of Lords surrendered their right to veto laws that that the House of Commons might pass. And 1792 France Leo 16 was beheaded and Louis-Phillipe stepped down before 1850 although Napoleon wasn't captured until 1870. Kaiser Wilhelm argueably ruled Germany and the Habsburgs Austria until the end of the First World War. Now America, as well as most of Europe, and democracy as its form of government instead of a monarchy. Yes, Queen Elizabeth still rules Britain and the entire British Empire, but most of the rights of leadership has been given to either the British Prime Minister or the head of the state of the "colony".
The Church, not claiming more land area other than Vactican City apparently agrees the civil / political power is better given to "the people" and not held by a monarch, bishop, archbishop, Cardinal, or the Pope.