I'd love a 600/4 with a built-in 1.4x TC. Not sure we'll see one soon, though.
Been wishing for this since the 200-400 w built-in 1.4 was announced. Actually, I think there is a good rationale for building a 1.4 into all the superteles above 400mm. The added weight/cost will not outweigh (puny) the extra usability for the intended consumers. I know I often switch the 1.4 on and off my 600 when stalking wildlife and it requires too much fiddling around - even if you get 'good' at it. I'm less enamored of the big zooms just b/c I need the speed and reach of the primes in 99% of my photo situations. Having a built-in 1.4 gives you that little bit of quick flexibility to frame the shot better. And quickly switch from say a whitetail at 40 yards (600) to a chickadee at 15 yards (840).
The problem is that the added cost to us is significantly greater than the cost for Canon to add the 1.4x TC capability. It is a cash cow for them and so it is no surpise they would want to extend this to longer focal lengths. Just don't be surprised when you see the price.
The Tamron can't get here soon enough.