You don't have to sharpen the whole blade with convex grinds. Those who assert you do don't really understand what's meaningful about the geometry. All sharpening occurs in two major stages: shaping and honing. Honing can be done just at the edge until the geometry has thickened to the point of meaningfully impacting cutting performance, at which point you'll go back to the shaping stage to restore the proper gross geometry. This is why understanding the role that specific geometry both at and behind the edge is so important, and these factors are largely ignored in favor of more readily observable cosmetic factors or superficial traits that are really unimportant except for how they relate to the fundamental root geometry.