There are MANY very traditional-minded priests (and bishops) out there that TRULY want them ‘in the fold’ and to have ‘regular status’ within the Church…
They are NOT schismatic, but rather “irregular”. They are NOT sedevacantists, and recognize the authority of the Roman Pontiff.
… but if there is to ever be reconciliation between the Holy See and the SSPX, one of the sides has to throw a bone to the other to get the ball rolling.
Not just MANY but almost every Catholic wants “them” in the fold. Each year some SSPX priests and laity come into the fold. They gain regular status, they now benefit, and benefit from, the ministry of their local diocese and bishop. They are not walled off into little enclaves apart from the other local parishes or apostolates such as prolife and religious liberty; the former SSPX people now fully participate, as they now come into the fold.
Some SSPX clergy, and certainly some SSPX websites, may not formally reject Francis as pope, but don’t really accept him as an authoritative teaching pope either. They may accept Francis when he happens to agree with them on what is true or important, but are not influenced by him in deciding what IS true and important. They may regard him as perhaps a valid administrator of the Vatican, but not fully a pope. The websites attack him, not obey him.
The Church has made more available the TLM and, if priests want to join, the FSSP. Some SSPX individuals come over; some don’t. The SSPX (as an organization) isn’t reconciling. Their leaders don’t want to give up their position, they want the Vatican to put its endorsement on the structure -
their leaders’ power structure - which would mostly stay the same. Its priests and laity would not benefit from fellowship with neighboring pastors, not benefit from the ministry of the local bishop, or Pope Francis, or Vatican II. If the Vatican did that kind of “reconciliation” with SSPX, other groups would petition for the same thing, so that you would have a “Call to Action” island in each city, each “protected” from the local bishop, etc, etc as many other groups would each demand their own enclaves, exempt from the local diocese. The SSPX leaders will never give up their power; they just want to keep the dialogue going, because it helps keep people from going over to Rome.