'Arnolds', at least that’s what I call them - a modified version of the dumbbell shoulder press. This is a modified arnold press as there is no back support. The problem with performing overhead press with back support is exactly just that…support. It is easy to rely on equipment rather than your muscles to maintain body position and alignment. Also strict overhead pressing keeps the moment arm for the erector spinae muscle group short, thus less demand. The problem with weak posterior chain muscles of the trunk is it could lead to the shoulders rounding forward, and the thoracic spine dumping into flexion. This can affect osteokinematics and arthrokinematics at the shoulder, which could promote poor movement patterns. SO why not perform an exercise to combat this from happening. You want an exercise that will increase postural and core demand while performing a shoulder press exercise.
Try out this modified version of Arnold presses. As I press the dumbbells overhead I am activating my core to maintain trunk alignment. This is even more important as I lower the weights so that my trunk doesn't dump forward intro thoracic flexion. Having the weights further out in front of me away from my body increases the moment arm (demand) on my trunk extensors!
We recommend endurance parameters for this exercise - perform multiple sets with a high # of reps until performance decreases. These muscles need endurance!