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Out of curiosity- since I still diver 10 year old Oceanic Air Integrated Nitrox computers which use the same algorithm as many brand new computers and do everything I need it to do- what is it that you wanted more of that you got with your new Shearwater?
Because it is easier to understand. The 1-button Oceanic computer sucks (press, wait, wait, press, wait, press and hold, missed the screen and have to wait for it to come around again, where is that manual?). Data logging the Oceanic is impossible now (it was a parallel port connection which no modern computer has). The user interface of the Shearwater works 100 times better. The Shearwater adds up your CNS and displays it. I have also transitioned into planned deco diving. It will store massive amount of logged diving, easy to download, has a battery life graph not just a battery good/bad icon. It is a completely different level of computer over the old Oceanic.
For really basic diving, the Oceanic worked fine. You got depth, and a little bar graph that climbs into warning and deco. For an occasional diver, it worked fine. For spending an hour+ in the water, with deco, and a gas switch, it is useless. That is why I got a Shearwater. Which I bring on my recreational dives as I like the info it give back better. And when doing deco diving I run a backup bottom timer and depth gauge along with a cut set of tables for the dive planned. The oceanic doesn't even come with me for those.
So while there are a lot of divers in the water with backup computers, there are most who don't. Out of all the stuff taught in an open water class, adding a second computer isn't one of them. Because for basic diving it isn't needed.
I did a liveaboard the other year. With just under 20 people for a week. All sorts of divers. From recently minted to instructors, kids, adults that needed all the toys, etc. I was the only one with 2 computers.
I'm sure there are a lot of divers out there they will tell you that it is needed, and a lot of them are probably just trying to justify to the world why they bought it. Not that they actually need it. When I got the Shearwater I didn't even think of it as a second computer, I got it as a modern replacement that could keep up with my transition into the tech world. But could still be used recreationally. When I started using it I kept the old computer just as a reference. After a little time I was comfortable with the new computer. At which point I had no need to actually remove the old computer, so it accidently became a backup. Wasn't planned that way, just happened. The used bottom timer/depth gauge was a planned backup.
Back to the title of this thread, "should I have a backup computer"
Eventually, but not now. When it comes time (if ever) you will know when it is time to get it. You won't have to ask.