The term 'Advanced' comes originally from the SVDX, beatmani, whatever games where the difficulty level itself vary from game to game. As well, Advanced works well as custom difficulty name if the difficulty feels too hard for a casual Normal difficulty level but too simple as casual Hard difficulty level. The bigger issue is if we start to include a difficulty between Normal and Hard that would mean this sort of difficulty will be necessary for mapsets since you are not allowed to skip difficulties in-between (example: Easy, Hard, Insane mapset is not acceptable for ranking)
Of course it would lead to a change to the rule but I also fear it will cause more trouble than necessary. Because they are custom it leaves us more room to make a proper spread for mapsets, and we should only use them if necessary or if fitting.