Genia kicks, and will continue to kick because Australia lack kicking options elsewhere in the backline, its that simple.
Surely he kicks because one of the jobs of the halfback is to be able to kick.
Every international halfback kicks regardless of the number of kicking options they have in the backline.
The box kick has its place and should be a safe clearance option with forwards there to give you some shielding and/or for contestable kicks because the advantage of kicking from the base is that the chasers are more further down the field already compared to chasing a kick from a ball that is passed back.
The charge down try when Genia attempted the clearing kick was presumably called by him. It wasn't like there wasn't another option or two set up to kick (Hunt and/or DHP).
His box kicking certainly needs a lot of work put into it. It seems like he's not kicking the ball from behind his body enough which is making it easy to charge down.