Pope Pius XII seems to speak of the Church as an institution of clergy:
19. The Church has, therefore, in common with the Word Incarnate the aim, the obligation and the function of teaching all (people) the truth, of governing and directing them aright, of offering to God the pleasing and acceptable sacrifice; in this way the Church re-establishes between the Creator and His creatures that unity and harmony to which the Apostle of the Gentiles alludes in these words: “Now, therefore, you are no more strangers and foreigners; but you are fellow citizens with the saints and domestics of God, built upon the foundation of the apostles and prophets, Jesus Christ Himself being the chief corner-stone; in whom all the building, being framed together, groweth up into a holy temple in the Lord, in whom you also are built together in a habitation of God in the Spirit.”[Eph. 2:19-22] Thus the society founded by the divine Redeemer, whether in her doctrine and government, or in the sacrifice and sacraments instituted by Him, or finally, in the ministry, which He has confided to her charge with the outpouring of His prayer and the shedding of His blood, has no other goal or purpose than to increase ever in strength and unity.
The fact of the institution is inevitable. And yet, it seems disappointing to limit the Church’s vector to the inside. An apostle to non-believers is referenced as a point of history. The threefold focus of doctrine & government, liturgy, and ministry point to increased “strength and unity,” but what of an increased reach and the mission to the ends of the earth?