Vatican I and Perpetual Successors: Does the Church Always Need a Pope?

Novus ordo apologists often accuse sedevacantists of heresy for allegedly denying the perpetual succession of Saint Peter. More ink has been wasted refuting this allegation than the matter deserves. Here, I'll limit myself to explaining the difference between
If anyone then says that it is not from the institution of Christ the Lord Himself, or by divine right that the blessed Peter has
If anyone then says that it is not from the institution of Christ the Lord Himself, or by divine right that the blessed Peter has
It implies that there will always be a pope at every point in time.
Explains that the primacy perdures equally in all successors of Saint Peter.
Our opponents often misread this passage of Pastor Aeternus, omitting the particle '
If anyone then says that it is not from the institution of Christ the Lord Himself, or by divine right that the blessed Peter has perpetual successorsover the universal Church, or that the Roman Pontiff is not the successor of blessed Peter in the same …