Here it comes, "I am a weightlifter". Their eyebrows raise in surprise and curiosity. "That is very interesting, not a lot of people that I know indulge in such a hobby". Your ego flourishes, until... "So tell me, how much do you bench then?"
Let me know if you find this familiar. You're in a gathering among people you haven't spoken to before and when asked what you do you answer as you've done for the last 10 years. And then, after a while, they finally they ask what your hobby is. You're dying to tell them because you're really passionate about your hobby and you have so much to tell them. You answer with confidence and a cheeky smile like you're about to baffle their minds with total, utter amazement! Here it comes, "I am a weightlifter". Their eyebrows raise in surprise and curiosity. "That is very interesting, not a lot of people that I know indulge in such a hobby". Your ego flourishes, until... "So tell me, how much do you bench then?" If there is one question that can get on a weightlifters nerves, it's that exact question. HoW MuCh CaN yOu BeNcH? Now, it's an annoying question not because one's bench press is weak, and even if it is, most weightlifters could not give a rat's ass about that. But because they never know what a weightlifter does. Of course, you'll try and explain yourself. "Well, I don't bench, I snatch and clean & jerk. by the way, It's also known by the name Olympic Weightlifting, if that gives you any indication of what my hobby is" Where they obviously start understanding the situation that is unfolding in front of their very eyes where they follow up with what they find logical in such a situation "AAHH So you're in the Olympics"... When your mind goes "Mother*****"
I'm not writing this to complain, but to tell you why most weightlifters don't bench press, or at least very infrequently. And yes, it is mainly for obvious reasons. It does negatively affect the overhead mobility more than 95% of any other movements. Overhead mobility is an absolute necessity, and anything that ruins, and at the same time doesn't have any direct benefit to offer, is likely to be rejected as a training modality. All horizontal pressing movements, not just bench pressing, and other movements that in some way, shape, or form could increase pectoral stiffness/tightness will not be utilised, or at the least reduced significantly.
"But bench pressing, and other chest related movements, increase shoulder stability". Yes, they do indeed, and step-ups increase leg strength! That is not to say that step-ups is the only exercise that increases leg strength, nor that it is the best one, nor the most specific for what the strength goal is. Yes, a bench press does increase shoulder stability and strength, it utilises muscles in and around the shoulder, but so does the overhead/strict press. For weightlifting, using the strict press, shoulder press, overhead squats, push presses, jerk recoveries, snatch balance etc. are specific movements to both strengthen, stabilise, and mobilise the shoulder joint, hence the reason they are prioritised above the bench press.
The pectoral muscles, pectoralis major and minor, have major implications on overhead mobility. But maybe not in the way that you think. Pectoralis major, the more superficial and bigger of the two is an odd one. Its got multiple actions, not just one. Not just two, nor only three, it can act in four different directions. Don't quote me on this, but I believe the pectoralis major muscle is the only muscle in the body that acts in four directions of motion. You see, because of its attachment on the humerus, a bone which makes up one part of the most mobile joint in the body, the glenohumeral joint, it allows for all of these movements. If the glenohumeral joint is placed in a position of extension the pectoralis major muscle will act as a flexor, a really strong flexor. This is where the bench press comes in. But in a position of flexion it acts as an extensor, only to the point where the arm is parallel to the torso (the same applies when it acts as a flexor). On top of these two movements, it also acts, alongside latissimus dorsi and teres major, as a strong adductor and medial/internal rotator. It's due to the two latter actions that it has MAJOR implications for the overhead position. See, when in the overhead position you're in a position close to full abduction (more so in the jerk than the snatch), and somewhere in between internal and external rotation. If the pectoralis major muscle is tighter than a gnats pisser you won't be able to get into a position of abduction and neutral "rotation". Don't tell me you haven't seen the chest Monday type dude in your gym who can barely face the phone in the general direction of his face and is unable to reach for his protein shake on the third shelf in the fridge without bending backwards in the process. Ask that guy to perform an overhead squat.
Furthermore, and since we're on the topic of chesticles, if the bench press didn't ruin the overhead position enough, the other satan possessed pectoral muscle is almost worse than the previous one. The minor, however, is a different beast. Its origin is on the anterior surface of ribs three through five, and its insertion is on the coracoid process. For you who don't know what the coracoid process is, it's worth a google. But I'll save you some time. The coracoid process is essentially a forward sticking part of the upper portion of the scapula. What? Yep, that's the shoulder blade. Although this bad boy rarely contracts in isolation, by that I mean the minor not the coracoid process, if overworked and it stiffens up it heavily, how do I put this lightly, F***** up the natural motion of the scapula. For it to even be possible to get into a proper overhead position the humerus has to move 110 degrees in abduction and the scapula has to upwardly rotate approximately 40 degrees. Now, here is the problem. If your pectoralis minor is pulling on the coracoid process into an anterior tilt, changing the position of the scapula that should sit firmly along the thoracic cage, then the upward rotation of 40 degrees that is necessary for a proper overhead position suddenly becomes a lot more difficult, and the subacromial space, the space between the humerus and the acromion, where the clavicle and the spine of the scapula meet, will decrease significantly. Resulting in a higher possibility of impingement or just straight bone against bone articulation, not ideal.
So to summarise, should a weightlifter bench press? Not unless he's willing to do the additional mobility work to maintain proper overhead positioning. Does the bench press negatively impact the overhead position? Yes, it does, but it can be counteracted with additional mobility work, as mentioned previously. Is bench pressing any good for weightlifting? It does have benefits, however, there are more disadvantages than there are advantages so you're probably better of doing some other exercises. Strict pressing would be a good choice.