For families that require 2D linework or masking in one direction only, or require different graphics in each view, it would be beneficial to have the option for front/back views to be independent, and left/right to be independent from each other. (Front, Back, Left, Right as separate tickboxes in 2D Visibility Settings, similar to the 3D Visibility Settings).
For example, Front elevation of a toilet has 2D masking and 2D linework, this is to simplify the graphics in view (as due to complex 3D form you don't want to see all the lines created on the 3D geometry), but as the 2D linework is visible front AND back, the 2D graphics can be seen on the opposite side of wall, especially if you have in-wall elements, like cisterns, plumbing or on some families, support structure, posts. Or you might just want to show part of the 2D opposite for coordination purposes (like an exclusion zone for the cistern).
It would save a lot of time to be able to control the visibility of items in view/plane within the family environment directly without having to resort to complex work arounds within multiple project environments (like having to create unnecessary sub-categories and multiple template views and having to put the responsibility onto general users, who don't have the same level of understanding about these 'behind the scene' things, (nore should they, their expectation is the family should just 'work'.) This is a great time waster for all users and we are all for looking for improvements and efficiencies in our workflows.
Having the ability directly set up and control these graphics within the family environment would be a massive improvement to project workflow and model quality and consistency.