There are a few assumptions that you make that must be challenged.
The SSPX did not "break away" from the Church. Because the Pope says something like that does not make it true. And the Pope was wrong on this. He is not impeccable on these issues. If he said, I went to Hawaii for vacation in 2003 and I didn't. He is wrong.
By all means read as much as you can about Pope St. Pius X. And see if you think he would be happy with allowing bishops to do what they have done. I really don't think he would've waited for Archbishop Weakland to turn 75 and retire peacefully after he paid $400,000 of hush money to his gay lover.
This is like saying the Eastern Orthodox didn't break away from the Church. They just continued believing what they wanted to believe, with their own ecclessiastical structure completely independent from Rome, under the leadership of bishops all of whom had been excommunicated.
If the SSPX did not break away from the Church, name one SSPX chapel that recognizes the jurisdiction of the ordinary in whose diocese it is located.