I know lots of people on MN love to hate on Prince Andrew but isn't that convenient for the whole RF? No matter what any other royal does, none of them is anywhere near as bad ...
King Charles has never liked him so this works perfectly for him. The press has completely convicted Andrew (and tbf, he's dug his own grave) and that means that Charles can largely do as he likes (bar that trickly lease for Royal Lodge ...).
Back in the day, newspapers reported on Sarah's 'scandalous' behaviour as a contrast to Diana ...
Looking at the Garter list on wiki, Andrew is not on it. So he is not blocking a place. And Charles can appoint anyone he wants whenever he wants: it is in the monarch's gift.
(and for the Princess Royal, 'on the blower' is exactly how she'll be communicating; like her father before her)
The most important bit of any title is actually the HRH, as we all learned, when it was Diana's turn and more recently Catherine's. That is what puts a body to the front of the queue and means that others will curtsey.
I think, technically, Sarah would be Mrs Ferguson Mountbatten. I read somewhere in some etiquette book ages ago that divorcées use their unmarried surname and their (former) married surname.
And there's not much point sending a message that his (past) behavour is unacceptable. It's in the PAST and now he's pretty much confined to barracks so can't manage much more than discomfiting Prince William at funerals.