The idea that Anglicanism just was invented because the King wanted a divorce is very simplistic and a Catholic myth. The bias towards Protestantism was already there in the 14th century in England with John Wycliffe espousing Protestant beliefs and translating the Bible into English for the Masses to read; a lot of it is due to the fact that England is pretty remote from Italy and didn't like having a Pope friendly with Spain, France, and the HRE meddling with it's politics.
Aside from Henry VIII, the logic of Anglicanism out of all Protestant sects is probably the most sound. Basically, Jesus established an institutional Church and consecrated Bishops who contained the fullness of the Church (which is basic Nicene dogma), but over time, especially compared to the Early Church Fathers, various Churches began to accrue a bunch of non-essential stuff (like mandated Latin, the Papacy, Purgatory, miraculous icons, types of bread to be used, etc.) that lead to schisms while the fundamental substance of the Faith was kept in tact, but because each Bishop comes from the Apostles and contains the entirety of the Church within their authority, the Church isn't actually divided here on Earth. Therefore, let's get rid of all of this non-essential stuff and be like the Early Church Fathers, so we can be as close to the Early Church as possible while minimizing divisions here on Earth.
The problem you get with Anglicanism though is that it begs the question of "what is non-essential and what is", such that you have High-Church Anglicans who believe it essential to pray to Saints and believe in a Priesthood; but you also get Puritans too.
It actually took the Papacy a while to respond to this and their response was rather than try to argue the logic of Anglicanism, they simply said that the Anglican Bishop orders were invalid because their rites deviated too much from the Nicene forms. But they had to admit the Eastern Orthodox Bishop consecrations were valid and therefore contained the Church, which created a logical error that Roman Catholicism still struggles with to this day as to whether the Eastern Orthodox Church is truly the Catholic Church or not - because technically, they are in schism and in mortal sin (And therefore outside the Church), but each of their Bishops are Catholic Bishops
(therefore contain the fullness of the Church). Pope John Paul II and Pope Benedict XVI called them Sister Churches, but if they are sister Churches, why convert? Aren't the Eastern Orthodox Church members saved? Why are we in schism then?
The Papacy also doesn't know how to address the Old Catholics who tend to have the Old Catholic Rite of Consecration and Bishops with Apostolic Succession, but are in the Anglican Communion.