I just tried to save my group’s settings without changing anything and, surprisingly, I wasn’t allowed to.
While it isn’t possible to save any settings when there is no owner and membership is granted by requests, you can easily remove the group owner from the group or revoke their owner status. In that case, membership request messages are sent to no one. Maybe removing the last group owner should be prevented if membership requests are enabled. Or is that a hidden feature providing a workaround for those who have asked to be able to manage group memberships without being a member of the group?