The soreness you are referring to is called delayed onset muscle soreness (DOMS) and is thought to be the result of tissue injury from excessive mechanical force, particularly eccentric force (i.e., the force produced as the muscle lengthens and the joint extends; also called the “negative” part of the contraction) exerted on muscle and connective tissue. DOMS is defined as muscle soreness that generally appears 24 to 48 hours after strenuous exercise. Typically, in order to experience DOMS from an exercise session, there have to be two factors present: (1) a stimulus that is greater than what the muscle is used to experiencing and (2) an eccentric component to the exercise movement.
The routine that you describe is a high-volume chest workout. If you are not sore after performing it, your chest muscles have most likely adapted to that stimulus and are conditioned enough to tolerate the work without becoming sore. Therefore, on a programming note, I suggest you mix up your workout with completely different exercises for the chest (e.g., push-ups and cable machine exercises rather than barbell and dumbbell exercises) or a different repetition scheme so that you are lifting heavier weights.
However, you also mention that your deltoids and trapezius are sore after this workout, but your chest is not. Without seeing your form, I would guess that during the chest exercises, you are allowing the shoulder blades to elevate, which puts more stress on the trapezius and anterior deltoids than is warranted. One way to correct your technique, and in turn put more focus onto the chest, is to perform your chest exercises with the shoulder blades set slightly back and down in the “scapulae packed” position. This will keep the shoulder blades set and stable in their proper position to allow the chest muscles to remain under tension throughout the entire exercise movement.
The second component to consider is the time spent in eccentric phase of contraction. You might try prolonging the time it takes to lower the weight toward the chest to really accentuate the eccentric contraction (e.g., lower the weight down for 3 seconds and then push the weight up for only 1 second).
Lastly, keep in mind that just because you are not sore after every chest workout, it does not mean that you are not getting stronger or fitter. Putting the time in to exercise is never a waste of time as long as your form and technique are proper. My guess is that you might have some mobility and/or stability issues in your shoulders that could be preventing you from performing the chest exercises you described properly. If this is the case, learning to pack the shoulders could help. It is also worth your time to seek out the advice of a qualified personal trainer who can look at your bench press mechanics and coach you in the right direction.