Arching on the bench press creates a favorable position for the shoulders.
The shoulder is the most mobile joint in the entire body. Benching with a flat back allows the whole shoulder joint to move freely during the bench press, which can excessively stress the connective tissues of the shoulder joint. That's what arching fixes: thoracic extension allows you to squeeze your scapulae together and pin your shoulders to the bench, immobilizing the shoulder joint. An arch on bench allows you to lift more weight for the same reason it is safer for your shoulders. You have a stable base, and instead of having to use your chest and shoulder muscles to keep your arms in their sockets, you use your upper back to leverage your shoulders into the bench, and your chest and shoulder muscles can work to move the bar, instead of working to keep your connective tissues from tearing.
That said, you do not have to use the acrobatic levels of arch often seen in the lower weight classes of competitive powerlifting. Enough arch to effectively pin your shoulders down is sufficient, which isn’t much arch at all.
In my own training, I do one session a week with maximal arch, using the heaviest weights. On the other days, I do lower weight variations with narrower grip and longer ranges of motion, such as close grip bench with bands and feet-up-flat-back bench.