Sure, but signed distance fields by definition have a constant gradient magnitude, aren't they? They measure the distance from the surface, which grows linearly

Sure, but signed distance fields by definition have a constant gradient magnitude, aren't they? They measure the distance from the surface, which grows linearly in the normal direction. But it is true that general implicit surfaces don't necessarily have constant magnitude gradients. I.e. F(x,y) = x^2 + y^2 - 1 vs. F(x,y) = sqrt(x^2 + y^2) - 1