The validity of the Jakubowicz result goes somewhat beyond its proof. Our two-dimensional geophysicist may be migrating other offsets besides zero offset. If a good job is done, all the reflected energy moves up to the apex of the zero-offset hyperbola. Then the cross-plane migration can handle it if it can handle zero offset. So offset is not a problem.
Difficulty arises when the velocity of the earth is depth-dependent, as it usually is.
Then the Jakubowicz proof fails, and so does the expedient 3-D method. With a 2-D survey you have the problem that the sideswipe planes require a different migration velocity than the vertical plane. Rays propagating to the side take longer to reach the high-velocity media deep in the earth. So sideswipes usually require a lower migration velocity.