It will be abolished when Christ returns and rules directly "forever and ever."
That aside, you are revealing that you do not really understand the extent of the schism with respect to the RCC doctrine of papal supremacy. It is irreparable.
Let me give you a different view: there will be a formation of a super world church consisting of a union between liberal ecumenical Protestants and the Roman Catholic Church, joining politically hand in hand, to create one of the most powerful religious forces on earth freely using the name of Jesus Christ: but it's going to be antichrist and political in many of its activities despite it's social action, charity, and ministries of compassion.
The pope will be considered more of a political than a spiritual leader of this great union. Protestant leaders of the ecumenical movement will insist upon and receive certain concessions from Rome in exchange. They will not be asked to consider the pope as the infallible head of the church and, in exchange, will accept his political leadership without accepting his role as Peter's successor.
I'm not asserting that the Pope in this super church organization will be engaging in antichrist activity. But an army of career people invading the most influential posts in this super church organization will be ungodly, antichrist people, obsessed with the concept that this super church must become a political power strong enough to put pressure on all those who oppose its actions.
While those in the highest posts of leadership will be speaking about miracles, love, and reconciliation the hirelings who work under them will be harassing and persecuting all Christian organizations opposed to their leadership. Homosexual and lesbian love will be vindicated by the leadership of this church union, including the pope, and will be both welcomed and encouraged. Homosexual and lesbian ministers will be ordained and given places of authority in this church union, and will be heralded as a new breed of pioneer introducing new concepts of love and evangelism.
Sunday school and church literature will be distributed in study curriculum asserting to children and teenagers that homosexuality is a normal and acceptable form of Christian sexual practice and most homosexuals will no longer seek help from the church as their sin will be defended by this super church as "gifts from God."
In some of the super church's member assemblies nude dancing will be excused as "artistic forms of worship." Men will become worshippers of the creature more than of the Creator, and God will be forced to give these kinds of worshippers
over to a reprobate mind.
The super church will condone certain occult practices (phrenology, palmistry, fortune-telling, horoscopes, etc...) in practice though it will never officially accept occult practices outright.
While all of this is occurring, a great and supernatural union of a
ll true followers of Jesus Christ bound together through the Holy Spirit and mutual confidence in Christ and His Word will become a kind of underground fellowship and will include Catholics and Protestants of all denominations. It will bind together young and old, black and white, and people of all nations.
While the visible super world church gains political power, this invisible supernatural church will grow tremendously in spiritual power. This power will come from persecution. The persecution madness that is coming upon this earth will drive these Christians closer together and closer to Jesus Christ. There will be less concern for denominational concepts and more emphasis on the return of Jesus Christ. The Holy Spirit will bring together, as one, people from all faiths and walks of life.
Although this supernatural church already exists around the world, it will become politically more invisible. But as persecution becomes more intense, this body of believers will become almost radical in its evangelistic efforts. This invisible church will receive Holy Ghost power to continue preaching the gospel until the ends of the earth have heard acting as a thorn in the side of the super church "coming out from among them" as ultimately, the RCC takes a negative stand against the Charismatic movement within the Catholic Church.
I don't believe the Papacy will ever be abolished, believe it or not. I think the true step towards reunification is a true Ecumenical council to discuss Trent. If that can be accomplished, then the field of play will change.