I wear my primary computer on my right wrist, so I can see it while operating my LP inflator. I keep it rolled towards the inside of my wrist, so that I can still see my depth if I'm performing a non-responsive diver rescue, which means being behind the diver and using my right hand to reach around and hold their reg in their mouth while reaching around with my left hand to operate their LP inflator (if possible) to control our ascent.
For me, I cannot imagine myself being in good horizontal trim, dumping air from my LPI, and being able to see my computer at the same time, if my computer were on my left wrist. I could only envision myself being able to see my left wrist if I went vertical or nearly so. And it would still be difficult unless my LP inflator hose were also unnecessarily long.
That said, I dive with 2 computers and put one on each arm, so I can conveniently see my depth on whichever arm is most convenient to look at.
I have never found it remotely bothersome to switch hands on the anchor line as I'm doing an ascent - even in NC or Saint Lawrence River current.
I got a couple of these 2 years ago. I think they were an LP Christmas special at $5 each at the time. I attach one to my camera and keep it clipped to my right waist D-ring. At some point during my ascent, I re-clip the quick release buckle and just let my camera hang. I never have to worry about dropping my camera. Meaning, I can drop it any time I want, since it won't go very far. With the QR unclipped, so the coil cord can extend, I never notice it pulling on my camera to make it uncomfortable to hold my camera out in front of me wherever I want it. I use one of these with my GoPro and another with my "real" camera rig with arms and 2 Z240 strobes.
36" Coil Lanyard