All characters on the same world should have automatic access to your private house, and should have a menu similar to retainers where you can trade items and gil.

I'm not entirely sure what the RMT concern is here, because you can already work around this limitation by listing junk for millions on the MB and then buying it up with another character, or by having your alt in the same FC and using the FC chest to trade items. So why the pointless roadblocks?