Use the power rack and keep the bar in contact with the rack posts throughout the lift. Imagine scraping the paint off the rack when you press. Push upward and slightly forward.

This exercise increases the activation of the serratus (finger-like muscles close to the rib cage). The serratus helps keep the scapula against the thoracic wall and increases the stability of the shoulder joint. Activating the serratus thus allows the shoulders to work better, making the exercise safer.

If you look at lean Olympic lifters who train the overhead lifts a lot, they have amazing serratus development which allows them to press heavy, often and without pain.

By pushing forward and up when you do the strip-the-rack press, you increase serratus activation over regular pressing. So not only will you activate it during your set, making the movement safer, you'll also develop it, giving you that superhero look by making your upper torso look thicker.

From a muscular development point of view, this press increases the recruitment of the serratus (giving you a thicker upper torso), pec minor (making the pecs look thicker), long head of the triceps (by doing an isometric shoulder extension when you push forward against the rack), as well as building the front deltoid.

Plus the strip-the-rack press keeps the muscles involved under constant tension. (You can even do partials at the end of the set, as shown in the video above.) Even in the parts of the range of motion where you exert less upward force, you're still pushing forward, keeping the muscles firing hard. This also contributes to making this exercise very effective at stimulating muscle growth.