This would be nice and even if they decided to put a $.99 pricetag onto it.
Given the widespread use of iOS (iPhone, iPad Touch, iPad) and Android devices (phones, tablets, netbooks), there's no reason this shouldn't be considered. EDIT: Blackberry too, I guess...
They'll get less complaints regarding being hacked, and less people will need to deal with the headache that is SE support.
Of course, this wouldn't fall under the scope of the FFXIV team as it encompasses Members accounts. No loss in dev time, more secure accounts? It's a win/win.