The reason the SSPX exists, by which I mean are tolerated within the conciliar fold, is because they do a good job of keeping people from the Resistance.
They give weaker trads coming from the conciliar church and discovering the TLM, who haven't fallen for the lunacy of Thucism yet, a sense that they are resisting, but also a sense of comfort, from the extremely worldly environment of SSPX chapels.
In reality it is all a show.
Take their recent "declaration" of fidelity.
https://sspx.org/en/news/declaration-catholic-faith-addressed-pope-leo-xiv-59110It all very good sounding, better than a lot of their previous squishy stuff, but all ultimately meaningless, as long as they continue with their marriage arrangements with the local diocese, and are open to a broader agreement, unlike Archbishop Lefebvre, who stated VERY clearly after the consecrations, that there was to be no more talking to Rome.