Right, the response time isn't the best. Before taking the actual picture, Canon code does a lot of preparations (including taking a dark frame at full width, but reduced vertical resolution, on most models). If you are in LiveView, turning it off takes additional time.
For instant response, you can try the silent picture module with the "Best focus" option. This should work very well for fast moving subjects running towards you, for example (use 50/60 fps if needed). Main issue: resolution.
The 4K branch has the potential to fix the resolution issue (it can take full-res LiveView frames on 5D3, but the focus estimation is not working yet in this mode). Pre-recording with half-shutter trigger can be helpful - it works with full resolution LiveView, but somebody has to port it on the 6D.