It would be nice to be able to have "clean" views of the public / family group tree by being able to "hide" inaccessible profiles. This preference should apply to the interactive "Tree" views, printing of trees, and (probably) to GEDCOM downloads. (By applying to GEDCOM downloads, I won't get a lot of "stub" profiles -- but perhaps the GEDCOM download could be a separate preference from the "viewing/printing" preference).
This should NOT be based simply on the private/public flag ... it should apply only to profiles which the logged-in user cannot see any details (other than F. NAME) because those profiles are both private AND not part of the Maximum Family Group (MFG).
Matches could still show the potential matches; that is a good thing (to know whom to contact if one wants to collaborate).