The importance of Fr. Karl Rahner, SJ, at Vatican II is generally known. His influence was enormous in the main official documents of the Council, especially Lumen gentium. Therefore, when he speaks on the topic, he knows what he is talking about.
In the text below he strongly declares that to consider that the Pope holds the supreme power in the Church is wrong. This supreme power would be a prerogative of the Bishops.
Such affirmation by Rahner frontally contradicts the infallible teaching of the First Vatican Council in its Constitution Pastor Aeternus on the Church.
At right, the cover of The Reform that Arrives from Rome, below right, photocopies from the Spanish original; below left, our translation of the yellow parts.
The Bishops are subordinate executives of the Holy Father in what refers to daily affairs; in this they submit to the central authority of Rome. The Bishops consider the Nuncio of His Holiness as his representative and their immediate superior. This concept is opposed, however, to Catholic doctrine. ...
The supreme power of the Church is exercised through the mediation of the Bishops; this was declared and reiterated with solemnity at Vatican Council II.
The first Bishops' Conference was held in Wurzburg in 1848 ...
With this precedent, the Bishops' Synod became a new form of episcopal collegiality on a national level. The Code of Canon Law of 1917 said nothing about this institution, but Vatican Council II declared it obligatory and permanent, enjoying all rights.
(Karl Rahner, "El principio sinodal," in La reforma que llega de Roma, Barcelona: Plaza & James Editores, 1967, pp. 20-22)