I think it'd be nice, as the leader of a guild, to be able to invite offline members; namely, your own alts.
My situation is that this week has been a little bit crazy in terms of scheduling, and my guildmates generally get on after I'm already asleep.
But, my character who founded the guild is level 19, and everyone else is max-level 7. So, I am making a new alt just to kick around, until everyone catches up to level 19 and I can take my main through a dungeon with my guild.
Long story short, I wish I could invite my own Alt to the guild... He would benefit from the perks chosen, and it seems strange that he'd have to wait for a friend of the leader to log on for an invite, when the leader himself really wants him to join! ;)