The only issue with that is you would immediately get friend requests from spammers or someone trying to "max LS" or other crazy junk. Unsolicited messages, especially ones that have repercussions that a player might not understand is a huge nono.

You should only be able to send friend invite requests while offline - AND they should auto timeout so they're not popping up all the time. If they do not accept the request then you can't send FC invites.

Another solution would be the ability to send LS/Friend/FC invites through the mogmail system, AND be able to filter them into a mail FOLDER.