At the start of a split, but not only at the start of a cut. The convex edge gives a thinner section for any given edge geometry when compared to a Scandi type single bevel. This means that you will have less binding and more efficient cutting. A flat with a flat secondary bevel will either have the same disadvantage of the scandi, or will have less metal in the head, making it weaker and a poorer splitting tool.
I know that progress only happens when people look at the world around them and imagine ways of making things better, but in this case I reckon there is good reason that the axe is ground the way it is. People have been using axes for thousands of years and I can't help but think that if a flat or Scandi bevel would be an improvement for general work, it would have had more of an effect on the tool's evolution. Instead, except for specialist purposes, axes have settled on a convex profile.
If you want it to cut better, just file it to a thinner conves shape. What is hard about sharpening a convex anyway? It isn't like you have to maintain a fixed angle
Again, generations of forresters have managed just fine with a file and a puck, so it can't be that tricky.