I hope the analysis is that the Epstein scandal was one of the major turning points in the public's perception of the monarchy leading to its eventual abolition.
Personally, I don't think it will.
I think Andrew is all but irrelevant now, to the general public at least. He is the most unpopular Royal by far. His unpopularity and actions do not appear to have impacted the perception of the RF, who are still viewed very positively since the Queens death. PA has been unpopular for a long time now, since his Airmiles Andy days, he just slumped lower down in most peoples opinion of him.
When the whole Epstein scandal is eventually and, hopefully, exposed. I think PA will be such small fry, in comparison to others involved, his relaltionship with Epstein will probably barely register.
I think it would take a huge scandal involving other much more senior members of the RF, for it to be a turning point leading to a possible demise of the monarchy.