Yet clean as the idea of groups was, it has been used only sporadically (in my experience).

As I recall it, the original "basic groups" were essentially "us" and "them". "Us" was everyone in the "in crowd", "them" was everyone else. Since the basic groups were rather extensive, it was prudent to turn group write permission off in your default umask. But that made groups rather clunky. You were in only one group at a time, so you had to "chgrp" to a select group, and then remember to set your umask to allow group write permission so others in the group could modify files. This changed when you could be in multiple groups at the same time (a BSD invention?), and your primary group automatically changed to the group owning your current working directory (iff you belonged to that group). This made it unnecessary to do an explicit chgrp in most cases. Having group write permission off in your default umask was now a nuisance. We fixed that by giving everyone an unshared primary group id, typically the same as the uid. It then became safe to make group write permission on by default. This made groups much more useful. Anyone in a group (but only those members) could create a directory owned by that group, and group members working in that directory defaulted to creating files (and subdirectories) group-owned by and writable by all the members of the group. It just worked.