DramaTom's OP aside, V1 explains it the best....
"If anyone says that it is not by the institution of Christ the lord himself (that is to say, by divine law) that blessed Peter should have perpetual successors in the primacy over the whole church; or that the Roman pontiff is not the successor of blessed Peter in this primacy: let him be anathema."
Not sure where this so-called "common sense and logic" fits into the teaching of V1, but they're clear when they condemn with anathema anyone who says that popes are not popes.
Yes, Vatican I teaches correctly that anyone who denies that the Roman pontiff is the successor of blessed Peter is anathema.
What you fail to realize is that
anyone who calls himself a "Catholic" already believes that to be true. The
real issue is whether or not the men who have claimed to be the Roman pontiff for so many decades are, in actuality, Roman pontiffs. If they are true Roman pontiffs, then to deny or disobey them would be anathema. However, that anathema does not apply to denying or disobeying false popes. Catholic teaching and history proves that these men claiming to be pope for nearly 70 years are false popes.
You also fail to realize that, when one believes in
every single papal power, it is
logically impossible for the men who have claimed to be popes for nearly the past 70 years to actually be popes. This is because those men who have claimed to be popes for nearly the past 70 years
absolutely contradict the preaching and teaching of
all of the popes who came before them concerning faith and morals. Since it is impossible for popes to preach and teach error regarding faith or morals, it is also impossible to even believe that these men claiming to be popes are actually Roman pontiffs, let alone believe that they must be obeyed in any way.
Catholic teaching for nearly 2000 years proves all of this beyond any and all doubt. For
anyone living today in 2026 as a self-professing "Catholic" who cannot realize this for himself is either of bad will or he lacks the intellectual courage to realize it.