It's not what I tried to say really. I'll try to explain. Rather than not caring about reputation, I'm not sure as to what exactly they can do to prevent massive botting to begin with. Other games would go for in-game tools selling in-game money for real ones (something what, iirc, WoW does, for example). I'm not sure now, but if my memory isn't broken completely, people asked about possibilities to have similar system in FF14 and the answer was no. And yet, it would have been the most efficient one - if people can buy Gil legally, there's no need for them go to sellers in general (though even then it likely won't solve the issue completely).
Another step is to prohibit using trading tools on free accounts - something what already is in the game so on this account they did it right (because otherwise it would be even worse than it already is). The thing is, without in-game erm... "gil trader", let's call it this, there's nothing really to stop the further spread, given that they can simply buy another copy of the game. You could of course hard-ban them by IP, but this will only result in hurting usual players, while bot-holders will simply use VPN and continue to do what they do. And this is what i meant by saying that situation is weird - there's no way to prevent botters from buying new copies, because you can't really say if a person is a normal player or not when they register their code on Mog Station, it's something what you can tell only later based on reports.
So the only option I see atm is to actually make their team that works specifically with bots and rmt bigger so there are enough hands to fight in the first place (you said yourself there are like, 4 people doing this, which is... nowhere enough in a game that became this big and popular). There may be better solutions (and there IS one, mentioned in first sentences) but for some reason they can't apply it, which is almost a shame, as I'm quite sure it would've been much more beneficial for them than botters buying base edition.