Summary They do not appear to be therapeutic to the shoulder joint. Doing them on wall was to supposedly lessen the damage and did not.
Snippets from article. Quite technical
We found that during a wall push-up plus exercise in healthy volunteers, the scapula was placed in a position potentially associated with shoulder impingement. Due to the shoulder kinematics of the wall push-up plus exercise, utilization of this exercise without modification early on in shoulder rehabilitation, especially in patients with subacromial impingement, may not be advised.
The push-up plus exercise is often modified to be performed against a wall in order to decrease the amount of weight-bearing through the glenohumeral joint and to avoid compression and further irritation of the rotator cuff muscles. The findings of this study of decreased upward rotation and increased internal rotation during the wall push-up plus exercise indicate that this exercise may put the glenohumeral joint in a position that decreases the available subacromial space and creates risk for impingement.16 Taking these findings into account, clinicians may want to reconsider implementing the wall push-up plus exercise, or modify the exercise to increase scapular upward rotation, early on in the rehabilitation of subacromial impingement. This is especially true if the exercise causes discomfort because it may further exacerbate symptoms and delay the healing process