You can say that the RCC needed “reformation,” but you cannot ignore the historical fact that for about 1000 years almost all Chirstians recognized the authority of the Pope and the Western church continued to do so for another 500 years.
Don’t get me wrong. I thank God for the political effect of the Reformation. Without it, there would be no United States. After all, once you can tell the Vicar of Christ to get lost, you can tell King George III to get stuffed.
About half of all Christians during that 1000 year period recognized the authority of the Eastern Church out of Constantinople.
Then there are the Armenian Christians who recognized the authority of neither, but they were never as populous as either the Eastern or Western Churches. But they still existed as an independent religion when the Western “Franks” of the Crusade came to the Holy Lands that they called “Outremar” or ‘over the sea’.
The grave difficulty with this analysis is that the earliest churches had no idea that a few, rabid folks were creating a central authority in a "pope". The word does not appear in any literature of reasonable authority until the latter part of the third century. The term "bishop" was interchangeable with a "presbyter" or "elder" and represented a description of the men at local churches identified with teaching/leading gifts.
Rome remanufactured this into a self-serving central authority, clearly contested throughout the ages by many local churches. That they dominated the landscape by brute force no more establishes their legitimacy than Hitler established his legitimacy in Europe.
And, even your math discloses that something was amiss from 1000 ad and following. Obviously, many brave folks were finally finding the voice to speak truth into the teeth of the oppressive rule of Rome. They paid dearly for such courage.
It was not, however, primarily political rule that needed reforming (but you're welcome for the U.S.). It was the mistaken theology of the seven sacraments, the sacerdotalism, the marioloatry, the indulgences, pergatory, penance, and (pardon the pun) a whole host of other errors in the manner the RCC represented the process of salvation. Those errors continue to this day.
The reformation set out in public view the Scriptural truths that undeserving men/women are elected before the foundation of world (Eph. 1) and that salvation is not a self-determined process like a business transaction (not wages, Rom. 4) wherein I exchange belief/trust/confession/actions/behavior or anything else originating in my soul for my rescue. Rather, it is the grace of God, through His Holy Spirit blowing where He will to make men alive from the dead (Lazarus imagery). Men and women are gifted faith to turn from self and cast themselves on the mercy of God, recognizing that the shedding of the blood of Christ (a one-time time/space/historical event) is the only thing that cleanses a man from sin and clothes him in sufficent righteousness to see God. They then begin the pilgrimage of beginning to recogize their rescue and are compelled to good works.
All repetitious chanting, confessions of sin, resolutions of heart, ceremonial sacraments are both ineffective and borderline blasphemous with regard to solving the problem of sin. Rome cannot give this error up because it is part of her hold over the supplicants. Tragic, monstrous, demonic. We call on Rome to repent...if she can.