Just came here with the same thought, that it would be better to have the default view on what is nowadays called “Public + Closed Groups”, thus introducing such an option. And removing the ambiguities around “My Groups”, which could be understood as what “Group I own” actually means, and “Closed Groups”, which could sound like they are no longer active, seems reasonable, too.
These sound a lot like:
- System Groups
- User Groups, “Public & Private Groups”, or just Groups
Maybe the order of groups offered in this filter item could be configured, with the first item always being the default view, so we can choose that. Else finding a suitable default order which works for everyone, plus allowing one of these view to be defaulted, would be another question.
Also, being able to give human-readable name aliases to “Automatic/System Groups”, for example some languages prefer capital letters in the beginning, as with the Full Name field in regular groups and providing them with optional, sane default description texts could render those appear less “technical”, if a site administrator doesn’t choose to explain them in their description via their Manage menu.
Maybe there could also be some kind of visual distinction between “Automatic” and “Non-Automatic” groups, like an icon, or their boxes being shaded in light gray, or something.