No picture profile can change the fundamental structure of the codec, plain and simple. Cinestyle is meant to mimic Log C curves, but technically are just "overcompensations" that mimic Log C within the standard rec 709. Detail in the shadows and highlights are there, only the camera's compression fucks everything up at the extremes of the scale, meaning the darkest darks and brightest brights become "lost" and clip. Cinestyle basically takes luminance values from the sensor that would normally be placed at these extremes, and compensates for this by placing them just outside of those values. So instead of dark sensor info being registered at the bottom, it is registered at the lower-mid.
Cinestyle is fundamentally flawed because you are relying on grading to make your footage look good, and relying on 8-bit h.264 is never a good idea unless you're in controlled environments (read: studio lighting) and are able to control color and values outside of the camera, and even then it's a pain in the ass. The only reason Cinestyle is getting so much attention is because people like Vincent Laforet are commissioned by Canon to endorse their product. They're basically payed to say good things about the cameras for marketing purposes.
Shooting "flat" can be extremely beneficial in certain situations, given that "flat" means you're using a normal picture style with the contrast turned down. Aside from that, unless you really know what you're doing when it comes to lighting/grading, don't even bother. Shooting flat in this case is one of those things where if it isn't going to be done right, you shouldn't do it at all.