The ONE thing I've noticed as a distinct advantage in a convex edge is, it can help prevent or reduce binding up of the blade in tough materials, like heavy cardboard, as can happen with a V-bevelled edge in cardboard, where the crisp-edged shoulders of the bevels add more drag and sometimes get hung up. You can actually see the cardboard get scrunched up at the shoulders of the bevels, if you've ever had a blade just STOP, mid-cut, in the cardboard. That binding up adds a lot of resistance to the cutting effort. The benefit of convex is more noticeable when the blade is relatively thick and the convexed 'shoulders' are mirror-polished; it can make cutting heavy cardboard a scary-slick experience. The best blades for cardboard would ordinarily be thin grinds otherwise; but, if using a heavier blade for it, convexing & polishing it can make a big difference.
Otherwise, a lot of the (debatable) hype about better durability, greater edge strength, etc., is usually overblown as I see it.
I see sort of a 'plus' in convex anyway, as it's a natural result of the freehand technique. To me, it's a more natural & simple blade/edge profile to maintain, in the long run. It's what our hands want to do anyway; therefore, more easily trained to do it well. ;