Dude from NC nailed it IMO. Wide boards change the plane of your stroke = much more strain on certain shoulder tissues because of the angle (also requires more external range of motion). Both the pulling stroke and the return are swinging out wide. Knee paddling fixes that. Or narrower boards.
I have a shoulder impingement & tears thruout labrum, rotator & scap, went to orthopedic shoulder specialist, cortizone shots, rehab & doc still wanted to perform surgery to relocate bicep tendon outside socket & clean up tears. No way was I gonna have major surgery w/ no guarantee of repair. When I was still dealing w/ pain it didnt matter what size board, the pain was close to intolerable. The only thing that has eliminated my pain was consistently do all the shoulder exercises I learned thru PT. Hanging from pullup bar (both dead hang & active hollow holds), external rotation exercises, pulldowns, wall shoulder raises w/ bands, list goes on. I can say that by learning these exercises & remaining very religious w/ them I have eliminated majority of pain. 2 years ago I couldnt even soft toss baseball to my boy & now I can throw longtoss with most of my strength & very little pain. Youtube & Instagram is your friend when it comes to learning these exercises and making them part of your daily life. $30 worth of bands & a dowel rod saved my shoulder & $10k in surgery.
My 2 cents as someone who has had a labrum tear and other shoulder cleanup work done: The weight of the board does make a difference. You are "Accelerating the mass" of yourself and the board when you paddle, particularly when sprinting to get out or to catch a wave. A heavier board requires your shoulders to do more work to accelerate your mass. To use a bicycle analogy you are trying to sprint on an old Schwinn Varsity (a heavy bike) in too hard a gear. All else being equal, a lighter, float-ier board is easier on your shoulder. I'll add that the water here has been unusually cold here lately, so I pulled out a couple of rarely used wetsuits and promptly hurt my repaired shoulder. It turns out that wetsuit fit has a huge effect on my shoulder comfort, and the Rip Curl mediums are significantly different (more restrictive in my case) than my O'Neill mediums. Instantly noticable difference in shoulder comfort!