I think this could be remedied simply enough. Instead of needing a user to 'be online' to accept a friend request, you could send the request to their mail as an option also.
(You retain the current way to make/accept friend requests - it's just you have a second option to do it via the mail moogle separately as well)

Log on 'you have a friend request' - accept or deny or block as options.
That way you can friend list your alternative account/s and send mail easily.

Unfortunately... the thought of 'friend request spam' comes to mind. Well there could be an option to 'Automatically reject friend requests via mail' - as I said above you will still have the current options for requesting while people are online so this will have minimal impact on players as well as retain defenses against RMTs and abusers/trolls/uglythingsthatgobumpinthenight.

Next is 'But it allows RMTs to transfer to each other easier' - Well... it becomes an issue of 'Anti RMT practices make it harder on players' - which is why it seems so 'Anti-alternative character' as the OP has put it... it is really not, but when the players support RMT - they will never go away and the majority who don't support RMT have to suffer for it :c