If the sole metric of the value of the press is its contribution to the bench press, then stop doing it, absolutely. And it's certainly easier to lay down when you press.
I'm now 50 years old, 6'3" and 250lbs.
I started the SS program in Mar 2012 after 4 months on my butt following achilles surgery.
With occasional 'slips' in progress, by Sep/Oct 2012 I was DL-ing 170kg, Squating 132kg, Bench 97kg and Press 70kg. No Clean due to the achilles thing.
I joined a powerlifting club and they moved me off SS programming onto something I still don't quite understand called Westside. The press was dropped. Accessory exercises were included - which really helped my bench. Other Progress continued slowly.
I've just been away for 6 weeks and hit the gym yesterday. I did a basic SS workout and managed DL 130kg x5, Squat 100kgx5, Bench 80kgx5.
I'd like to get back to the club but want to restore my lifts to where they were first.
I'm wondering if I really need the press?
Given that it doesn't feature in the powerlifting meets, and my bench progress was better when I dropped it for other assistance exercises (eg: close grip bench, incline db bench) I wonder how necessary/useful it really is.
And since the bench is an exercise that could, potentially, be included in every workout - at least at my level - wouldn't I be better off sticking with that?
If the sole metric of the value of the press is its contribution to the bench press, then stop doing it, absolutely. And it's certainly easier to lay down when you press.
I feel like someone may have written an article about this recently.
I find that pressing without my shoulders helps prevent shoulder injuries.
Fast forward to when OP starts having shoulder problems...
As a former volleyball player who didn't train during my playing days, I've noticed a correlation between the lack of shoulder pain I have these days and my press. Weird.
I also notice a correlation between my improved balance and my adherence to squatting. Even more weird.
Do rows and other similar movements not strengthen your rotator cuff muscles?