I see that this is forbidden for the purpose of beautification. What if there is a different non medical reason why one would want to shave that area. For example if the man or woman felt it enhanced their physical pleasure when having relations?
The reason that it is permitted for medical reasons is not because it isn’t for beatification, but because it is evident that it isn’t being done in order to appear womanly, but because there is a specific need to shave over here. Therefore, shaving that area, when for a different reason would not be permitted. This would only apply to men, but not to women as it is a womanly thing to do.
Shulchan Aruch Y:D 182-2, Shach ibid 5, Darcei Teshuva ibid 5, Conversation with R’ Y. Scotzylos author of Ohel Yackov – Lo tibash.