The value and importance of the press has demonstrably shown to be absolutely priceless for shoulder health, upper body strength, as well as developing the courage to forcefully move a (heavy) object overhead.
The top position of this movement has one important cue: "LOCK THE BAR OUT!"
Why should we lock the bar out on top of our head?
Three simple reasons:
FULL TRICEPS ENGAGEMENT
As we know, one of the movements the triceps perform is elbow extension, i.e. "locking the elbow out".
When we extend the elbow at the top position, we work the triceps through full extension.
Full extension means greater muscle activity and greater strength in this range of motion.
Remember: In strength training we want to work our muscles through the OPTIMAL range of motion.
Locking out the elbows mean greater strength the triceps in the fully extended position.
BETTER SHOULDER HEALTH
Together with the triceps locking out the bar, the UPPER TRAPEZIUS muscles elevate the shoulder joint. This is one of the natural movements of those muscles.
When the shoulder joint is elevated, the acromiom (which is the highest point of the shoulder - easily palpable as the top little point as you touch your shoulder above your middle deltoid) gets pulled away from the clavicle, which creates space in the so-called acromioclavicular cavity. This is the area most prone to impingement syndrome in which the tendon of the supraspinatus muscle gets trapped.
Bar lockout --> trapezius evelates shoulder joint --> space creation in cavity --> no impingement.
As we lock the bar out overhead, the shoulder joint performs a movement called INTERNAL ROTATION.
Internal rotation allows us to keep the bar perpendicular to the body.
In other words: the bar is "balanced" above our head in the most stable position.
Further, the prime internal rotator muscle called the subscapularis pulls the humerus into the glenoid fossa. That means the actual bone of the upper arm is "locked" into its socket.
The foto below depicts the anatomy of the subscapularis (Note how it inserts on the humerus to the left and by contraction it would pull this bone into its socket).
Picture this as an example: when you lock the bar out on top, a solid force vector is created from the bar into your hands, into the triceps (as it is fully contracted when you lock out), into the internal rotators of the shoulder joint, moving all the way down into the scapula, the spine, the pelvis, and the floor - creating a solid position which is locked in from both the top as well as bottom through ground reaction force.
If we want 100'% results, we need to give 100% care to details.
So lock the press and shoot up your strength.