I've actually found the full auto mode to be useful when I want someone who has no camera knowledge to snap a photo of me or my group. Instead of trying to explain to them how to focus ect, I just throw it in idiot mode and it usually comes out great for a quick snapshot.
Agreed - I've used the green square mode that way a couple of times. It's especially nice because I use back button AF, and I like that it still shoots in RAW.
Of course, the 1D X doesn't have a full auto mode that cancels out back button AF. Nor does my $20 RC-1 work with it, so I can easily get myself in the shot, even if I did bring my tripod. Sacrifices I'm willing to make. Fortunately, in situations where I would like to have a complete family snapshot, I usually have my S100 along, and that's plenty easy for a random person to use.