When Pope Pius XI established the Feast of the Kingship of Our Lord Jesus Christ, with his 1925 encyclical Quas primas, he did not choose the last Sunday of the Liturgical Year (as later done by Paul VI). He chose "Reformation Sunday" which Protestants celebrate on the last Sunday of October, to propose Christ as the Anti-Luther.
The Lord is not the King of this or that German prince who changes doctrines according to the whim of the moment. He's the King of the universe, unchanging and unchangeable. Pius XI proposed the Feast of Christ the King as a counter-celebration to the Protestant celebration of "Reformation Sunday" on this day.
Source: Scuola Ecclesia Mater