Pembina,
The long hose is used in overhead situations because it's quite impossible to air-share in a lot of the situations we face while cave diving if you're using a standard length octopus. It's completely unnecessary for OW divers as there's no need to air-share through restrictions or while swimming in an overhead. According to my training from both PADI and SSI, I can see a point to being close to your buddy in an OOA situation. That's a whole other argument though that has been beaten to death on these boards. I still use the long hose for OW diving, but that's to stay in practice/it's what I mostly use. I was skeptical when I was first introduced to the concept of wrapping a 7ft hose around me, but frankly, it works.
Still, with coming off the left, what do you do if you need to use that backup reg for yourself? Now it's twisted around in front of you, which is a lot more awkward than a bend in the hose giving it to the other person. Something to think about. And if the regulator ends up in their mouth upside down it's still going to deliver air just fine. There are also in-line octopuses which means you can just jam it in their mouth without worry of bends, upside down, ect.
About recovering the reg, it's really a non issue if it drops out your mouth. In my PADI OW class, to recover it, all we did was lean to the right, sweep our hand down our side, back and out and then forward making a big "U" next to our body, which your primary would simply "fall" into. I never had a problem grabbing my octopus instead while doing this since it was attached to my BC within the "triangle."
I'm wondering if you were taught a different method of recovering your primary, and maybe that's why you think there might be an issue with recovering if your octo is on the same side. The way I was taught is a slow, smooth, deliberate motion involving no grabbing at all, really.
I don't think either right hand or left hand is more prone to dying than the other. What's important is making it as uncomplicated as possible(no clutter around what you're reaching for in a stressful situation) and practice.
Me personally, I've never seen the hose come off the left and it's fairly foreign to me, just as off the right is to you. I haven't done very many OW dives with divers using "traditional" setups though, so my exposure to such would be limited. Just about all of them since dive 11 have been with others preaching the long-hose method.