There is absolutely no reason the Canon 5D MkIII should not be able to record 1080p @ 60fps. The Digic V has sufficient processing power. 1080/60p would most likely have to be limited to IPB compression though, as ALL-I would require a sustained write speed of about 23MB/sec.
Has anyone taken a look at the Sony a77?
It's a $1400 body with a 24.3MP sensor.
It records 1080/60p/60i/30p/24p and does so with an inferior processor to the 5D3.
It's simply a limitation of firmware. Canon purposely crippled the camera to protect their higher end models (which most considering the 5D3 can't afford anyway). It's not like people in the professional market would stop buying C300s, C500s, and 1DCs if the 5D had more advanced video features. The pros are still going to buy the dedicated cinema cameras for the expandability, advanced manual controls, and I/O features (HD-SDI, XLR, Genlock, Timecode).
And yes, I realize the 5D3 is a photo camera first, but 1080/60p is not something that would handicap, or take away from its photo abilities. It wouldn't even cost extra!