Having dual card slots for instant backup is great, of course, but before we go out of control with paranoia, remember that not much more than a year ago all of the wedding photographers shooting with 5DII (including myself) somehow survived.
The 6D (through wireless - as has been pointed on on this thread) actually has much more flexibility for backup than the 5DII. I shoot weddings with two 6D bodies and have not yet had an issue.
Yup, dual card slots is one of those things that has only been around and affordable for a short while, but now that its here some act like it's always been here and your a fool to not use it.
And yeah, after renting the 6d, my only concern/worry was the sd memory. My solution has been use nothing larger than a 16 gig card (i have mostly 8 gig ones), the best ones i can get (i favor the lexar cards for both SD and CF), and then just be really careful when dealing with them.
All that other stuff, not paranoia but just pointing out that lots can happen on a 12 hour day, yes one could be card failures, but other stuff can go down. I had it happen to me 3 weeks ago, had a saturday wedding, and shot an event friday night. Halfway through, my trusty used 580exII simply dies (af beam fired, all the back controls work, so i think its the flash tube, still have to call canon to see if its worth it to have it repaired.) So between the salon and picking up the second shooter i had to do the emergency run and spend way more than i wanted to that day on a 600rt (which i will say is a better flash than the 580, kind of glad the 580 died because if not for that i would not have been able to justify the upgrade).
Either way, the point is that we try within the best of our capabilities to plan for the unexpected - which is worse, having a back up with sd memory, or no backup at all? Little things like - if i had ponied up for a second 5k3, then that would have meant no advertising in the local paper, and ---probably would not have had the extra cash kicking around to snag the replacement flash. Not to mention the evil eye i was getting from my fiancee when i'd bring up the second body issue. It took a lot of talks on the porch to convince her that the 6d even was a valid and needed purchase.