Interesting. I never thought of it that way for a few reasons....
Although V1 was permanently cut short, it still gave us the dogma of Papal Infallibility. No one knows what else it would have given us if it was not cut short or was continued.
V2 came at a time in history when drugs were becoming more and more popular, rock and roll more vulgar, hippies more ugly, there was the flower power and free love, Vietnam war, JFK αssαssιnαtҽd, MLK / Civil rights, riots, and a multitude of other major social scandals and distractions were all going on at roughly the same time. Enter V2, they added their chaos into the mix at the right time - it all fit. I believe too many of the faithful were growing more and more lax in their faith, so God gave them what they wanted, so to speak.
The reason I say they got what they wanted is because the very few faithful who would not go along with the new religion were very often persecuted by those who went along with the new religion and for remaining steadfast and stubbornly clinging to the only faith they ever knew, refusing to go along with the crowd.
So IMO, I believe the people back then who went along hold a big chunk of the responsibility for what V2 did - and that V2 or something like V2 was bound to happen because of the laxity, or perhaps unfaithfulness, (or sins?) of the Catholic people.