What you just stated doesn't make any sense in the benefit to Canon in sales. If a new camera offers around the same performance as the 5DmkII at a similar price... then why would people buy it? They would just keep using the 5DmkII. So if Canon were to do exactly what you stated, they would have to spend a lot of money in developing, testing, producing, and marketing a different camera that would hurt their existing 5DmkII sales (since they are keeping the 5DmkII in production in the forseeable future). Note that Canon has not indicated that the 5DmkII will be discontinued when the entry level FF camera becomes available.
What if Canon discontinues the current 5DII?
Canon could use the current 5DIII sensor, a morphed 7D-like AF system and maybe something like no video. Throw in a current Digic5 and lower the FPS.
Then, put it all into a current chassis and sell it as a new model for $1595. The 5DII (or, another new model variant) could still be sold including 5DIII-like video features at the $1995 price point. This is actually pretty easy to do because most changes are in the firmware. Heck, Canon could include the hardware (video jacks for example) but disable it through the firmware. If you want to upgrade your "basic" FF camera, send it in to enable the firmware. This elimiantes 2 production lines and parts groupings. Win Win, as long as the firmware upgrades are possible in the future, even for second or third hand equipment. Just like computer software, there would be a point where upgrades on old gear is not possible.
Those that need what the 5DIII offers will buy that model instead. Therefore, it will not cannibalize 5DIII sales, but rather gain sales from those that can't swing or justify the 5DIII price point but still want the full frame experience... and more importantly, may be willing to choose a different brand.
Increased production of the 5DIII sensor only lowers costs and increases market share.
I predict that a ~$1500 basic full frame camera aimed at pictures and no (or limited) video would sell like hotcakes. What brand will release one first?
If Canon wants to increase market share, they need to do this. Once someone is invested in accessories, making a brand switch is more difficult.