The papal faction and the "papal bull" function are two separate entities. I believe you can remove the papacy by following ECS' advice regarding keeping them out of Rome. With the papacy faction removed, the "papal bull" function should stop as that's what usually happens, without having been in Rome though they shouldn't be able to reappear as Rome is their "emergence" province as Switzerland is for the Swiss, Burgundy for the Burgundians and Khazar, Armenia, etc for the Golden Horde. You can test this easily. Remove Rome from the Papal faction's list of provinces from the startpos and place a strong rebel garrison there. Then start a game as the italians and wipe out the papacy and see what comes of it.
When the papacy reappear, they do so as a "new faction" (like when the golden horde appear) not as a loyalist revolt triggered by the presence of an under age heir and loyalty in former provinces below 120%.
Only in Switzerland and Burgundy and only if loyalty is below 120%.
And +1 command star.
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