The loss of jurisdiction means the loss of Apostolicity, which is one of the marks of the Church. Holy orders are simply not enough; one needs jurisdiction as well. With the loss of Apostolicity the Church loses the other marks (unity, catholicity, holiness). The Roman Pontiff is the perpetual principle of Unity, through which apostolicity continues, as infallibly declared in Vatican I Council. The jurisdiction granted by Jesus Christ to Peter and the Apostles has been handed down by the successors of St. Peter in all generations. This is what Vatican I means when it says the Popes shall reign in perpetuity.
Thus during a Papal interregnum (when a sede vacante is possible) ordinary jurisdiction continues through the Church herself. Some misguided people would say "oh, the Church supplies jurisdiction", but that is not accurate. Supplied jurisdiction comes about through a confusion due to a particular law, and it flows from the Church's ordinary jurisdiction. If a whole generation has had no Pope, then Ordinary jurisdiction has been lost, which means there cannot be supplied jurisdiction, meaning the gates of hell would have prevailed against the Church.
What sedes propose is a complete new religion, not different from a Protestant sect.