Just to be clear, are you saying the Church, as Christ founded it, no longer exists?
No. The new covenant cannot be and is not over, and the gates of hell have not prevailed and will not prevail against the Church.
That there is no longer a Church that can legitimately carry out the mission that Christ entrusted to it (which requires legitimate authority)?
No, I don't subscribe to that proposition. My conclusion is: Currently, seats are occupied by apostates or modernist heretics. So currently, the Church isn't carrying out certain tasks which are reserved to legitimate occupants of the seats.