“Of course, as an aside, Father could ask the historical Protestants “on what basis did/do you believe you have the authority to leave the Church, and reject apostolic succession?” This line of questioning (IMO) would lead to constructive criticism of those churches which hold to solA scriptura”
By the same Authority that Christ himself broke with and denounced the religious authorities of his day, by pointing out the hypocrisy of their lives in line with what Moses and the prophets had actually written in the old testament(sola scriptura argument), not by what talmudic traditions had taught.
When the Catholic Church suffered its biggest schisms via the Reformation, it was in a sinful state. The “shepherd” had been struck through her own sin and arrogance, would you not expect the sheep to scatter and attempt to gather around its strongest remaining Rams?!!
Furthermore, your example falls short, on the grounds that, from all eternity, Jesus knew that He would be establishing a new covenant in His blood, and the Law, which had hitherto sufficed, would now be replaced by Grace, won for us on the Cross. A new order had to be instituted accordingly, and the old order, now rendered insufficient for anyone's salvation, not just that of the Jews, was to pass away. Besides, on a relative scale, the Jews of Christ's time were much more faithful to the God of Abraham - even taking into account their hypocrisies - than their forebears before the Exile were, so it wasn't so much on the basis of widespread infidelity that Jesus supplanted their rule.