I do not see any reason why even beta should have "JO". Beta sites have 2 or 3 characters (see other sites). The same is for minor SE sites which do not get their own icons longer time after beta phase. So if this icon will be with us longer time, why not to adjust it? The sooner, the better.

technically there are possibly more icons, but they all look the same: (1) the favicon (2) site icon in list of SE sites in dropdown menu (3) icon at StackEchange sites page (4) meta.joomla.stackexchange icon (black) (5) sites list in your profile and maybe some more