The term convex edge is hype. A convex edge adds nothing to the way a knife cuts. All things being equal, a flat ground edge will cut better than a convex edge inside the same dimensions. Its the technique used in making an edge convex that adds to the sharpness of an edge; its not the shape itself.
True flat edges are harder to produce than convex edges because, any deviation from the desired angle, when sharpening, will alter the apex. With a convex edge technique being used, this problem does not arise. The apex is always being contacted.
Convex edges are fine, there is nothing wrong with them at all other than the fact that they are never the same; they change as different pressures are applied against the abrasive being used.
A flat ground edge, on the other hand, can be reproduced over and over with out deviation from there norm if a proper technique is used.
Fred
PS If a convex edge goes half way up the primary bevel everything written above is moot.