It really is common sense.
Once a group puts itself under the authority of modernists, it's not going to break away again. So what will happen? The same thing that happened that caused the group to believe it could remain traditional and be subject to modernists. That is, a break-down of the intellect and will, a failure to continue to understand the traditionalist position and a lack of will to remain steadfast in it.
Once under the modernist the leadership will gradually devolve to be the choice of the modernists.
This is all so obvious.
The desire to join with Rome is really the desire for liberalization and acceptance.
When the SSPX became about belonging to a group instead of being Catholic, it became very vulnerable to such tendencies.