I thought the entire point of the curvature map was to control the angle at which it happens? There isn't any control over it's parameters. How is this any different from AO? (other than it's only self-referential).
From my layman's perspective, AO looks for occlusion, it doesn't care about surface flatness. Curvature map does the opposite - it looks for surface flatness and doesn't care about occlussion. The fact that highly curved surface is almost always self occluding, makes AO look similar to curvature, but in fact those are quite distinct maps and their output can be tuned to serve different purposes. Angle threshold control would be interesting to have and already has been requested, but to be honest i didn't see such control implemented in any curvature map (not that i saw many of them), maybe it's technically hard to implement, or its usage is not very practical?