To be safe without being a pain, Nintendo needs a parental block system. The parents could program the console to block out chat, customization(like Emblems on MKDS), and even Wifi altogether if they're that paranoid. Nintendo could even put an instruction manual where it is clearly visible that says Parents: Read this Before Giving this System to your Child or something like that on the front that teaches parents how to program the parental system. They could also have a video tutorial on their site. I know nothing's idiot proof, but as long as Nintendo makes it idiot proof enough, they shouldn't have to worry about their young audience playing Wifi games. It'll at the very least, let Nintendo keep their image and all that stuff.
EDIT: instead of the game systems themselves, Nintendo needs to do to the games for now.