[sudosysgen]

That's not how it works. If I take a picture with 2x crop sensor at 100mm f/2 it is going to be exactly the same picture as at 50mm f/4 on a FF camera. Its just how it works. They have proven it using the DOF equation by showing that scaling the CoC factor down with the focal length and scaling the focal length down means you have the same DoF as long as the actual aperture diameter is the same, algebraically. I gave you an explanation of why it is the same because the solid angle is preserved. In the end you're making the typical photographer mistake of misunderstanding crop factor.