shut down valave doesnt require positioner as noboady controls it . Limit switch gives the information whether the valve is open or close. Main purpose of shutdown valve is incase of air fail the valve closed promtly or operator can close it through soleniod.
you may require to operate sd valve at some percentage opening at a partila failure of a loop to prevent some downstream equipment , like open the sd valve 50% one shot if a particular compressor surges etc. Then you require positioner,
If you do not need control of the sd valve at any stage and its only for the full open close methodology then the positioner might not be required since it will only add another instrument to the loop that may fail, so one needs to make a descision based on the requirement of the process, Always better to keep number of components in aloop to the minimum to increase reliabilty, reduce downtime and also troubleshooting time.