Notivago, you must have been told in your open water course that you have to plan every dive, regardless of whether you use tables or a computer to do the planning! Wearing a dive computer to keep track of the data related to the dive does not imply that the diver has no need to plan the dive. You must also have been told that regardless of the means used for planning the dive, the most conservative device used amongst those in the buddy pair/team/group diving together is what everybody follows. If one diver is following tables and the other is following a computer, the one following tables will control the dive; if both are wearing computers, the diver with the more conservative computer controls the dive.With tables, you have to plan for the dive, you go down with your limit already set, when you get to the limits, even if your gear is acting up, others will signal to you to either come to the proper depth or stop at the proper time. And if it all fail, tables are more conservative so you have more leeway.
With computer you can simply dive to the limit, and if it acts up, there is no way you can double check its results, you have to thrust in it and you will be walking a lot closer to the edge as they are less conservative and thus you are more prone to accident.
I like safety, so I like a saying from a friend of mine: One equals zero, two is good.
I don't see the computer as a substitute for the rest of the gear, I see it as a very cool redundancy.
Since you have such a distrust of electronic devices, I hope that the timing device (watch or bottom timer) that you use to track your dive time is a high-quality mechanical one rather than a battery-operated electronic one, and that unlike a great many inexpensive mechanical timing devices, it keeps accurate time.