“The Church of Christ, by the revelation and institution of Christ himself, is essentially visible; and this visible Church is the Church to which his promises pertain; promises, namely, that she would be perennial and indefectible, and that in her and by her men would find sanctity and salvation.” (Billot, Tractatus de Ecclesia Christi, vol. 1, 3rd ed. 1927, )
This is laughable, since this is precisely the core thing that Vatican II rejects. But, aside from that, you again try to reduce visibility to some guy walking around Rome in a white cassock. Besides that, where to we find "sanctity" in this Conciliar Church?
That's only one aspect of visibility, with profession of the truth faith, communion in the same Sacraments, etc. all being aspects of visibility.
With your reduction of visibility to the material hierarchy ... to the exclusion of these other aspects ... the Church would defect during any given interregnum, and much more during a lengthy interregnum. We've had Antipopes usurp the Holy See before, have had the Great Western schism, where Catholic were in doubt about where this "visible" Church was, have had nearly the entire episcopate go Arian, during which crisis St. Athanasius made his famous statement about the visible Church being potentially reduced to a handful of faithful. As I pointed out before, the
ad absurdum of your principles would have had the True Church becoming Arian and would have put the orthodox bishops, priest, and faithful OUTSIDE the Catholic Church had the Arians succeeded in getting one of their own on the See of Peter.
What if bishops like St. Athanasius and others who went around consecrating parallel Catholic bishops for the sees that had been usurped by Arians? Were they schismatics also? What of St. Vincent Ferrer, who adhered to an Antipope? There have been many Antipopes, some of whom were accepted as Popes for some time in Church history. Where the material Church resided has been in doubt numerous times in Church history, and so it is again today.