Yes, that's what protecting itself means. In this case things have become so public that the best/least bad option to protect the King and the Prince of Wales is to sacrifice Andrew.

I'm not so positive that's the case. It's fairly well reported that Andrew and Charles have not seen eye to eye for...many decades. Charles kept the peace probably for his mother's sake while she was alive, but even before the major epstein revelations, Charles had been pushing Andrew to the side