Brake shudder does occur on any kind of brake (coaster, disk, drum aside) but is more pronounced in occasions where unsheathed brake cable travels further to the rim.
As a fork flexes as its meant, the longer cable is set under higher tension momentarily, braking harder, and deflexing the fork. Then tension is reduced but the brake is still applied and the fork rebounds back again.
A lower mounted cable jacket using the fork mount mentioned by the OP can significantly reduce shudder (not eliminate it) by lowering the amount of movable cable between the brake and lever when acting across a flexing joint.