Well, wow.
Ladislaus, I know you have difficulties with the R&R position, and we've discussed some or most of these elsewhere. You still misunderstand what canonists and theologians teach regarding the distinction between convalidation as a cause of an election acquiring validity and universal acceptance as a sign and effect of a valid election. I think I cited at least 5 authorities explaining it elsewhere. But that's not the point here.
This thread is entirely about the reasons for the first R, why it is necessary to recognize the Pope. It is self-evident that it is necessary to resist error, therefore to prove the second R, and thereby the R&R position (and what you are attacking is a strawman and a misrepresentation of it), it is only necessary to carefully define after that, according to pre-Vatican II teaching, in what circuмstances, teaching and acts a Pope can be questioned and resisted.
In particular is a rejection of the claim that an interregnum can be indefinitely extended. In the past, you have yourselves said it is probable that the Church would defect in a 100 year interregnum, or at least a 500 year one, and asked for a definition of what the limits are. So I put you on the spot and ask you why you think an interregnum cannot last forever, if formal Apostolic succession can indeed be continued apart from the actual Petrine succession.
I say that it cannot, for only a Pope, and certainly not a heretical non-Pope, can appoint bishops to offices, and all offices or episcopal sees cannot be vacant, otherwise formal Apostolic succession has ceased. In this way, the Apostolic succession and the Petrine succession are inextricably interconnected.
Likewise, only a Pope can incardinate Roman clergy, and Roman clergy cannot cease to exist, as St. Robert taught, Pope Sixtus IV defined, and Msgr. Fenton among other theologians explain. But if all the acts of the non-Pope grant neither stability nor right to anyone, those he attempts to incardinate into the diocese of Rome are not really incardinated. This then is another reason why an interregnum cannot continue indefinitely.
There are two consequences of such an absurdity, that the Catholic Church will cease to be Apostolic, and that She will lost Her Roman character, both of which are impossible. Therefore, an interregnum cannot be indefinitely extended. Can we agree on this much?
This is not something exceptional or strange, because it is a defined dogma that Peter must have perpetual successors, that what Christ has established in Peter and the Roman Church where the Petrine succession is continued must "of necessity remain forever" (Vatican I). It is a condemned proposition that "There is nothing whatsoever to show that the spiritual order demands a head who shall continue to live and endure with the Church Militant" (Constance).