Source Cropped slightly from PIA22956-16.jpg
It actually does have a wrist joint. To quote NASA's about the lander page:
The arm is 5 feet 9 inches (1.8 meters) long, with shoulder, elbow and wrist joints and four motors. The grapple is at the end of the arm. The arm-mounted camera is between the elbow and wrist.
The wrist joint does however not seem to be used for the deployment. The grappler is just hanging down from the end of the arm, no pivoting is needed here. All it does is lift up and set down objects.
(Image Credit: NASA/JJP via spaceflight101)
The joint seems to be used for the "bucket", the black box at the end of the arm. It can be seen in different orientations in different depictions.
(Image Credit: NASA via SEIS homepage)
To quote the SEIS homepage:
Besides the gripper, InSight's robotic arm also has a bucket with a capacity of roughly 500 g of soil. However, this bucket is not intended for massive excavation works; its main role is to prepare the ground as well as possible before setting the instruments down. It allows engineers to shift a stone that is in the way, flatten a little mound in an otherwise optimal deployment sector, or simply check the nature of the ground.
This image from a paper describing the arm shows the four joints. The wrist and elbow have one degree of freedom, the shoulder has two.